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1 . n h rn c 9 n h I a : A B , va BC h I a : al n h dl nh B, din h C Ba g 6c I a : g6c dln h A; g6c dln h S; g 6 c al n h C • Ducmg c a o c u a ta m g iac I a OO(:l n t h a n g ke t u mot dln h va vuong goc v6'i c� n h doi di� n (c� n h day). H c DQ d a i cua dliong ca o Ia chieu cao cua ta m giac. M¢t ta m g i a c c6 3 duang cao. 2. Ta m giac ABC c6: A H Ia chieu cao t u'ong ung voi c� n h day BC; A Bl la chieu cao tuang ung v6'i c9 n h AC; CK I a c h ieu ca o tuong U'n g v6'i c9 n h AB. Ch u vi: P = a + b + c (P: ch u vi; a, b, c I a a(> dai ba c9 n h ta m g i a c) Di$n tich: 8 == AHxBC BixAC CKxA B _ _ S 2 2 2 s X 2 h A s X 2 tro n g a Ch .1 e u cao h = -- ; Cc;I n u a y a = -, h- ; u oA h I ' c h 1eu cao tuong ling c9 n, h a. "' , . . A' a 3. Ca c d� ng ta m g ia c H1 n h ta m Hin h vu6ng Hlnh can Hlnh tam giac cteu (c6 m¢tg6c vu6ng) (2 cgnh nhau) (3 cc;mh bang nhau) A rc h i m ed es 3 A s c h o o
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A RC H I M E D ES SCH O O L I L c A. c o�NG sAt TAP A . T in h c a c yeu t o cua ta m g i a c Bai 1 . D i e n ket q u a v a o 6 trong (v6i a I a ch i eu d a i m¢t C9 n h cua hl n h ta m g ia c v a h Ia c h i e u ca o tlfon g U'n g cua c� n h do). �--- -- ---· -----.....---------,-- - --,--I \ 400cm i O,Sdm 3,8m . 7 c m a I I l I I ! l l 1 1 I I h 25 cm li 4d m 2 5 d m 2,5 dm · �-----s li I 2 1 c m 2 L4 d m2 I l . _ __ _____ ...... . .. .. . . Bai 2. f)ien ket q u a vao 6 trong (v-ai ta m giac vu6ng). - C� n h g6c 2 5 rn 5 ,2d m 4 5 cm vuong 1 '""··· ··· ................., C�n h g 6c 1 8m 4d m Sdm vuong 2 - -·· __ _ __.......� Di�n tich 9 d m 2 1 00 c m 2 I t a m q i a c ·····�·�·········· Bai 3. Tfnh di$n tfch tam giac/ biet d9 dai m¢t c�nh Ia 1 2cm va chieu cao tVdng U'ng Ia Scm. Bai 4. M9t tam b ien bao g iao thong hl n h ta m g iac c6 tong c9nh day va chieu cao tvang ung Ia 32m, C<;l nh day hon chieu cao S m . Tfn h d i� n tfch tam bien ao . Rise above oneself a n d grasp the world
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n 2 Lf n d d n 3 h ca n h tam n t a m c a o g L 3 --- ------------ - ---- - M <?t thva r u (? n g hl n h ta m giiK v u o n g c6 s o do m ¢ t C<;J n h g6c vu6ng I a 8,4m; s6 ao c9 n h g6c v u o n g con l� i ba ng 7 5 o/o so do c� n h da biet Hoi di�n tich cua thlra r u ¢ n g ba ng bao n h ieu met vuong? B a i Tfn h di$n tfc h p h a n to d� m biet: BM 9cm; MC = 4cm va d i � n tfch hl n h ta m = giac ABM Ia 27cm2• · B
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ARC H I �/1 E O ES S C H O O L . Toa n s - Quyen 3 . 1 s. M ot h! n h giac b.3 n g ?_ chieu c a o tuong N eu B a i 1 5 2 . Hi�n n a y I ii 5 g i b'. H o i sau it n h at bao l a u n Qa t h i k i m p h C1t va· ki m g id v u o ng B a i ta m c6 c<? n h da y un g . keo d a i can h. 4 g6c vai n h a u ? day them Scm thi d i � n tic h c C1 a hln h t a m g iac ta n g them 30c m 2. Tf n h d i �? n tfch hl n h ta m g i a c do. ·�- . ····---- ---- ·- --- - ·------ - -- · ·--- -- -- --- - ---·--- ·----------- ·· · · ----- --- ·--- ----�-- --- --- ------ B a i 1 53 H i � n nay I a 1 o giO'. Hoi sa u ft n hat bao L3 u nua thl kim p h ut va kim g i o vu6ng .. vuong d a i CO g 6c v6i n ha u ? Bid 9. C h g m¢t ta m g ia c A BC a A. N eu keo AC ve phfa C m9t do9 n sao cho AC = CO = 8cm th1 di�n tfch tang them l 44cm2• Tfnh d9 da i C<? n h A B va di�n tich tam g L3c Vuo n g ABC. B a i 1 54. Hi$n g io dong h6 chi du n g 1 0 g io. Hoi thO'i g i a n ngan nhat d e kim g i C1 va ki m phut thang ha n g voi n h a u? Bai 1 o Cho tam g iac ABC c6 di�n tfch 60cm2, c� n h BC dai 1 Ocm . .. a) Tinh d<) d a i auong cao h a t u A xuong c9 n h BC. b) Gqi M Ia tru ng ait�m cua BC.Tfn h d i$n tfch tam giac ABM. c) Gqi N ta tru ng ctiem cua AC. Tln h di�n tfch ta rn giac A B N . andR ise a bove o n eselfg rasp th e world Arch i med es School I 67 Asc h o o l .ed u.vn ,
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x e p 8 Bai tam: c N en SCMN = s - (s ·?sMC + SDNC) ABCD A1vlN + AM = 1 6 (em); BM = 32 (em); N O = 1 2 (em); AN = 24(cm) 728( ) =�xAMxAN �x16 ( ) Bay gio Ia 1 2 g io. Hoi ft nhat bao I a u sa u kim g i a, kim p h ut tru n g nha u ? S = AB x AD = 48 x 36 = 1 cm2 ; SAMN = x 24 = 1 92 cm2 1 ABCD SBMC = ..!_x BM x BC= 576(cm2 ); SoNc _!_ x DN x DC= 288(cm2) = 2 2 ' ( ) ( ) SCMN = 1 728 - 1 92 + 576 + 288 = 672 cm2 fJapso: 672 cm2 A BAI T�P Bid 1 1 " Cho hln h ve ben, biet SABC 90cm2; - = - ' 2 , ' = 3 5cmi. Tm h SANe Bid Bay gia I a 2 giO'. Hoi it n hat bao lau sau kim gio, ki m p h ut vuon g g6c n ha u ? SABM ; SAMN = -SABM " 1 5 c ..
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ARCH I M ED ES S C H OO L Toa n s - Q uyen 3 , 1 B i d d i� n g i a c AECG . B i et h l n h H . Ch.uyen d9ng c u a v �t c 1 2 . T f n h tfch hl n h t lf 1 4c nl 8 :_: h l£ n h � t ABCD c 6 A D -= 2 0 c m ; A B -= 1 4-c m ; B E = Scm N\ ¢ t I va n-1 ¢t c¢ t di e n h et g i a yl di m9t c3y c,� u d a i 45 0 m . Ba i 1 46 . xe di q u a 20 q u a h et v a DG = 9cm. chieu 6 5 g i ay. Tln h d a l va v�n toe c u a X P l tJa . ---- --.- 2 00 1) ------�--- --- · D 9cnl __ ____ · ..:!_ SAse Bai 1 47 . M¢t doa n tau h6a dai 200m ch�y qua m<)t c3 i ham. Toa aau vao harn k: c 1 0 B a i 1 3 . C h o t a m g iac ABC (hl n h ve ben), biet 51 = ; 9 . gio 48 ph ut,\ toa cu oi ra kh6i h a m l u c 1 1 gia. Moi giG' ch9y dtifjc 27km . ll m ch i e u t a u 53 2 va 52 d ien tfch tam g iac dai c u a ham. = SABC = 20 cm2 • Tfn h . A BC. 9 A c B a i 1 48 Mqt 6 to di v&i v�n toe SOkm/h vuqt qua m¢t xe Ilia di cu ng ch ieu trong 3 6 .. Bai 1 4. Tinh di�n tich tam giac ABC, biet: 51 =J_SAsc g iay. Tfn h chieu da i cua x e hJ'a, bit?t v�n toe cua xe I U'a Ia 40km/h. 6 Archimedes School 1- Rise a bove oneself 6 5 and gra s p th e \Norld Aschool.edu . v n
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n g 3 toe c A q _) i\ BM , S '-\BC I; a, I a 1 = 2 x1 1 AH Ta c o : SABM B M ; s - X X 8( �- - --- -�-- ' X ABC ---- 2 --- 8 c S B M , , S C M => � = - La m tuan g tlf, ta co : ACM = - SAac BC . SABM BM Chu y: Hai tam gi6c c6 ch ung au&ng c a o thl t1 /e dien trch bang tl l� cgnh Clay tuong ung. 1: Cho hl n h ve ben, bh?t BC = 3MC va S = 1 8 cm2 ABC Tfn h SAMe 1 M Qt n g uoi ai tu A de n B g o m m 9t doq n len d oc va m <)t do� n xuo n g doc. B a i lam: · V� n toe khi l en doc Ia 3 km/h , v� n toe khi x u 6 n g doc Ia 6km/h . Th ai gi a n ai c u a ngVO'i sAMe =MC _2. cao h a tv den BC) = (Ch u n g duan g . A f d6 1a 3 g i o 3 0 p h u t va thoi g i a n ve Ia 4 g io. Tfn h q u a ng cluong A B . / SABC BC 3 �x18 B H c =�SAac = 6(cm2) SAMe = A B a i toan 2. Cho tam giac ABC, M tren can h A B, N tren can h . . T'a nh S AMN Ac. • -- .. S Afl( , Ta c6 : SAMN -- A M . S ABN , -- - =>A N SAMN X --=SABN AM X - => -- = - X -AN SAMN AM AN -- - -- -- - B a i 1 A n d i tren- m¢t do9 n dVO'ng A B g a m m¢t do(;ln l e n doc v a m 9 t do�n uong SABN AB S ABC AC SABN SABC AB AC SABC AB AC x · d o c. Thai g i a n ca di lan ve I a 8 g i o. Biet ra n g l e n d oc vcri v� n toe 3 km/g io va ai b" A, 1 1 Vi dl;l C ho h>1 nh ve b Ae nf ret AM = - AB A N = - AC va 5 48cm voi toe 7km/ AB d a i bao - 2 ABC -- 2 A xuong d oc v� n g iO'. H o i q uang auon g n h i e u ? 3 ' Tfn h SAMw Ba i la m : ..:!_ _2. � Ta c6: SAMN = AM x AN = x = SABC AC 3 2 6 1 1 2 S = -SABC = - x 48 = 8cm AMN 6 6
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ARC H I M E D ES SCH OOL _ Toa n s - Quyen 3 . 1 B a i t o a n 3 . C h o ta m g i a c A BC, M t re n C C:l n h BC, N tn ? n AM . F . V� n toe t r u n g b ! n h , - , So sanh s " tlf'.l s ,.BM V� n toe = to n g to n g -- - v a -�--- .. t rung bl n h q u a n g auon g : th 0i g i a n 5 /iCN s .ii.CM Biti 1 40 . M r) t n g uoi eli x e m a y di t U' A den B d a i 240 k rn v 6i v ,§ n toe 40 km/g id. 8i dude Ta c6: �_A§,'-:1__ 8�� --=> s B M 5 = C M ABM = M x ACM n lia ouong , n g lioi d6 t � n g v� n toe t h e rn 20 km/gid den B . rln h v� n toe t r u n g bt n h s C ACM � - cua n g udi d o tren OO-? n dU'o n g A B. SNBM BM B M 5 -- · -- = -- ..........; SNBM -- - X NCM SNCM CM C M BM (. . 5,.1\BM SNBM ::::: X 's -SNCM ) s s ___; C M ACM BM s = -� . =? ABN = - ::::::::;> ABN - BM . ·S SACN CM .SACN s X. ACM SABN - CM ACN Vi du 3: C h o hl n h. ve be n , biet BM � BC va = 3 A Ta c6: B a i 1 41 . B{t n An di tu A den B voi v�n toe 6km/h, s a u d6 An d9p xe tu 8 ve A vdi v�n toe 9km/h. Tfnh v�n toe tru ng bl n h cua An tren q uang avong ca di lan ve. -S · - =ABN . --SABM = ·- =BM -1 S ACN SACM CM 2 M 1 SACN 20cm2 SABN = - x 2 = Bai toan 4. �ho tu g ia c AB DC c6 d i�n tfch Ia 1 oocm2 ... h ve- en , 1et - T., .... h t . , . A (ht n b"' ) b · �' AH = - �3 an h d "· "'ten ttc a m g rac O K 2 . • :\'-. l' : // ! '·····-,."'' ABC. / ··"-.: I/ ·-...., Ba i 1 42. IY! Qt n guai· ai xe d� p tu A den B . Kh i kh6'i hanh t<?i A, ng uoi d6 c1i voi v� n toe /1/ Ta c6: = 2_ xDK x BC 8 .. K 1 Okm/h, n h un g tu ch fn h g i ua dvang den B ng uoi d6 di' vc:fi v?n toe 1 5km/h. Tfn h v � n SABC = � x AH x BC; SsDc /''· 2 2 LJ I t o e tru n g bl n h cua n g u'oi d 6 tren c a qua ng duong AB. SABC - AH --3 -- -3 s -3 - ( ) -- - 1 00 - 60 C m2 '. => SBDC -.DK- - - =>2 5ABC 5 ABDC - - X5 ' ··-,_"L/ Ch u y.wHai tam gidc c6 ch ung cgnh day thJ tiI� di�n tfch bang D ti l? 2 duang cao tuang ung. Rise above onese lf 1 63 Arch. imed es S c h o o l a nd grasp the wo r l d Aschool .ed u.vn
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n o 1 g n1 g IV1 L?l l 9 n p c a n h N P s a :J = = i n a) ---- - ---- - --- --- ---- b) S CAN = 3 c - -- ------ sCAP -- ----- ----------�---------- S CPN = S C NB ---------------c----- 6. C h o ta m g L :§ c A B C c6 d i � n tfc h 1 8cm 2, t re n A 1 M 9t c a n o di -<uoi d o n g tu A den B vdi v� n toe sokm/g i a. Di n g vqc d o n g t u B c9 n h BC l ay di e m M s a o ch o BC = 3B M . Tfn h d i � n tfch den A v6i v�n toe 40 k m /g i a. Biet thai g i a n ai xuoi d o n g ft hO'n t h o i g i a n di n g llQ'c ta m g ia c A B M . do n g I a 30 phut? Tfn h d¢ d a l q u a n g auong AB. c 1 Ch o tam g iac ABC, tren c� n h B C l ay 3 diem M, N, P s a o cho B M = M N = NP = · PC. Bietdi�n tkh tam giac A M N Ia 1 2cm2� Tfn h d i $ n tich ta m gia c A B P1 A BC. Bai 1 39. M9t ca n 6 d i xuoi d ong tu A den B tren m¢t kh uc son g mat 3 gia va n g uqc (Chu y: Ve h inh tnroc khi lam bai) do�g tu B tro ve A mat 5 gia Tfn h chieu d a i kh u c son g d6, b i et v�n toe c u a dong . n vac Ia 60m/ph ut. R i s e a
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A RC H I I\1\ E D ES SCHC)fJL E . C h uyen d9 n g t re n d o n g n uoc sa i 1 s. c l· 1 o V • ·J o i :::::: Vthuc + f1 tiOC \J ng u'qc :::::: ) . . "'- n c!f)c = (Vxubi Vngur;rJ : 2 ····· -- - - - -· ---·-··---- Bai 1 3 5 . L(te 7 g i o, rn(lt thu ye n may di xubi dong tu ben A den ben B c u a ' , --··- - --- -- ---- t huy'- n. 6 m a )- I I '. a -> --? S km!" g t o .l v� n toe·" d 'on g n U'O'c' i 'a 2 2 k, m / g J a... · - ··--·-··- ·-···- · ··- -- · . . A ···- -----·--·--- - · _ - ·· e may den B . Hoi: - t h u y · n -·--· ·· ····- - - ------ ---·-·--···--- · · a) Th uyen Ol dy' den B h.Jc m ay g io? b) Do dai q ua n g song Ia bao n h h � u kHo-lTl et? --- --------·· - ·-- - -- ·· · ·· --·- --- - · --- -- ·--· · ·· ·· ·- · ·· AD = = FE = Tfn h - · DC, BF EC. Swc ; Sot:::: . --- . ......................................_____ -- . .... ...................---------- · · - . . ---------------------------·····----··-···----· ----··-------- · __;:_______ ---- ____................................___ ··-------- ----------- ·------- . . . . · ··----·--···-··---·-- ...... ............ . ...--------- B a i 1 3 6 V� n toe dong n uoc Ia 1 8 111/ph (1t. I\A¢t nguoi bol xuoi q u a n g song d ai s o o rn .. � CM ,1 AN = M N . Tin h het 8 phut Hoi n g u'oi o6 bo'i nguqc dong qu��ng song a6 het bao n h i e u t h O'i gia n ? Shew L.. · · · - - --· - - · - ···- ·· ---- ·· --- ··-- - - -- ---- --------'---- · - - - - - · �-------- ................................................................... ---------·---··---····------·-·--·· ·--····-·-·---·------------- -··· · ____ ------- __ _.................................. . . . _ ___ · - -�-· - · - · - --·--· -·-·----·- ---···- --------· ·-·-·····-- ·---·----····-·---·- - ----�-- - ---·· ··---·--·-· ···---- ----·····-·-··-·---- · · · . -·- -- · ·- ------------- -------- ------ ·· - --- · --·------ - -- --- -· - -- · - ·· - --- - - ···- · · - --·--- ·- - · - ·- - - ------------- l I A rch t m ed es .School 1 2 Rise a bove oneself . :t' I a n d "� rasp the world Asch ool.edu.vn .
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g c;, a o o - - ----- ----- s. a o \ 8 C: ---- - ---- --------- --------- --------------- --- -------- L u e 7 g i d m9t xe m ay di t v A voi v� n toe 40 krn/h. Ben 8 g i G' 1 5 u t m ¢>t o to cu n g �i tu A vO'i v�n toe 6 0 k m/h va di cung ch ieu v6'i xe m ay. Hoi den m ay g id 6 to duoi k! p xe m ay? -- - -------------------- ------- B iJi C h o ta m g ia c A B C ( hl n h ve b e n ) . Biet AP = PC, A A M = MN = N B . Tfn h: SAMP p a) = SABC N ------------------ b) SAN? = SABC B c ------------------ c) SAMP = SACN ------------------ Qu a n g duO'ng AB d a i 1 ookm, cung m ¢t l uc xe 6 to di tU' A va xe m ay di tu B . Bai 23 . Cho ta m g ia c A BC, die m M n a m tren c�n h A B Neu d i n g vqc c hieu, h a i xe se g?p n hau s a u 1 g i o 1 5 p h ut. N e u di c u n g c h ieu, 6 t o sao cho AM = BM, di_em N nam tren c9 n h AC sao cho auoi theo x e may thl s e g � p n h a u sau 5 g i O'. Tfn h v�n t o e x e 6 to, x e m ay. � fv1 A N = AC . BiE!t SAMN = 1 0, 5cm2 , tin h SAoc. B �-----------------------·-·· c a b ove oneself the world
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1\ R CH I M E D ES SCHOO L Toa n 5 Quyen 3 . 1 -- Bai 1 30 . H a i 6 to 6 A va B ea c h . n h a u 7 S k m c u n q kh oi h a n h m Qt l u c va ai cung c h i e u I A Bai 24. C h o A M C M , N B i'lM , B P � BC , d i en tich ve g io tlt A d u o i T1 m v� n t o e m o i 6 bi€t = = ,� p h ia C . S a u 2 , 5 thl 6 t o d i k i p 6 t o di t U' B . t o 3 BN P b a ri g 3 c rn 2 . Tin h d i � n tfc h q i i K A B C . ra. ng to n g h a t v� n toe I a 1 1 4k m / h t a m g i a e t a m M ----- -----�---------- -- ----------- B P Ba i 1 3 1 . Qua n g auang A B dai 90 km. C6 hai o to c u n g x u at phat n1¢t l uc ?:J A va 6 8, ai c u n g chieu ve p h fa C. S a u 4, 5 g i o 6 to di tl.r A duoi kj p 6 to cti tu B tS�i C . a) Tim van. toe cua moi 6 to, biet ti s6 van. toe cua hai 6 t6 Ia � . A 4 Bai 25. Cho tam giac ABC (hl n h ve ben) c6 AM = M N b) Tfn h q ua n g duong BC. = N B, A P = PC. Biet sAsc = 1 20cm2 • a) Tin h SAMP ' SBcN b) Tfn h di�n tfch tu g i a c M PCB, M N C P . c) Tinh SMNP c B Bai 1 32. M(>t xe may ai tl.r tln h A den tin h B v6'i v� n toe 45 km/gi0'. Khi xe may di duqc 1 g i a 3 0 -ph ut thi m¢t 6 t6 di voi v�n t6c 70km/gid tv A au oi thea xe m ay. Biet h a i xe den B cung l uc 1 1 g io. H o i : a) Tt n h A each tln h B bao nh ieu ki l o m et? b) Xe may da khoi hanh tu A l u c m ay g io? 14 1 I R ise a b ove o n eself Arch i med es S chool 59 .. . a n d g rasp the world Aschool.edu.vn j
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s n h s .\i3C = n S a u o i - BC . g n _-:: 4 s t = (_ 1 Lu c 7 g i o, n g udi t h v n hat di tv A vdi v� n toe 1 5 km/g i0'. Cung t9l B each A 7km, n g voi th li khoi h a n h va di cu n g c h ieu vdi ng vbi t h v n ha't, v6i v � n to e 1 1 km/g i o. H 6 i h a i n g voi g � p n hau l u c m ay g i o v a diem g�p n h a u each A b a o n h i e u ki-1 6-met? 27. C h o ta m g ia c ABC, tren Ci?nh A B l ay dh�m A 1v1 sao cho AM = M B; tren cgn h AC· Iay diem N , P s a o cho AN = N P = PC. Tlnh s biet N Asu SMNPB = 1 2cm2 . /_::,./'_ ..... ....---- B _ _. � � ( ···· ----·· · · -- Bai 1 29. M¢t 6 to di tu A du o i theo m9t xe may tu B (hai xe cung khoi h a n h m<?t l u c) va sau 2,5 g i o auoi kip xe may t�i C. Stet v� n toe 6 to Ia 65 km/gia, v�n toe xe m ay I a 45 km/gio. Tin h q u an g duong AB. B a i 28. C h o t a m giiK A BC (hl n h ve b e n ), b i et AM == M N = N B, A P = PQ QC. Biet 52 - 51 = 1 2cm2 • Tfn h di�n tkh tqm = g iac A BC. a b ove 5 g rasp
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ARCH I M ED E S . SCH O O L · oa n 5 - Qu yen 3 . 1 !-\ B a i 2 9 . C h o :.:: QP = PC; A M = MQ; A N = N P v a d i ¢ n t!ch M N PQ l ,3 : 3 c m 2 . Tinh d i ¢ n tich - N -- - -- ---··-- --------- ·--- - - - -···---· · -- ---- ta m giac A BC. 8 c Q p ------· - - ---------------·-·---- Bai 1 26 . (Ams 08 - 09} Tren quang duong AB dai 1 .20 km c6 h a l n g uoi di ng uc;tc chi e u n h a u. N g uai th u nhat di t u A bang 6 t6 vdi v�n toe 60 km/h . Sa u do 1 5 phut n g udi t h v h a i di tu B ba ng xe may voi v�n toe 40km/h. H o i :; a u 1 g i o 30 ph ut ke tu l uc n g uai th v hai· khai h a nh/ khoang each g i ua hai ng uoi Ia bao n h i e u k i -16-met? -----·-·--------- ----- Bai 3 0 Cho tam g iac ABC. Biem M n a m tre n AB sao A .. cho AM = 2MB. N Ia tru ng diem AC. f) i e m P n a m tn§n chd 2. Tfn h SMNP /. BC sao B P BC. ti l e ··,, N • = 3 SAOC ' ----�---���:.r -�., . M/{-.-----------··-- _..·· / .,_ ./_.�-�-/ __ -----------.· -� c- B ../ . P Ba i 1 27. (Ams 09 - 7 0) Cu ng n·1¢t luc ng uoi thu nha� ai tu A den B va n g VO'i th u hai d i t v B ae n A, h a i nguoi g?p nhau t9i c each A m ¢t ao?n 4km. S a u d6 nguoi th u n hat di den B roi q uay ngay I C? i A ngay, n g u'ai thu h a i di den A r6i quay ngay l�i B, hai ngVO'i g�p nhau I an thu hai t9i D ea c h B m9t do9 n 3 km . Tfn h a<? dai quang du'Cin g A B . Rise a bove on eself Archimed es Schoo l I 5 7 and g rasp th e world Aschool .ed u.vn
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6 f l O s 1 = B u t p h x e , n 6 t 3 x e B P C P 1 Luc 6 gia m (?t xe khach kh oi h a n h tu A de c:ti den B vO'i v � n toe 60km/h, den 6 g i a 48 p h ut m<)t x e kh a ch kh ac k h oi hanh tu B di ve A v&i v� n toe 5 5 krn/gio. H a i xe g f? p n ha u l u c 8 g i o. Tfn h q u a n g dtJC1ng A B . B a i . Cho ta m g iac ABC, tren c<? n h B C lay diem M A I a tru n g ciie m c9 n h BC, diem N nam tren c� n h AC sao cho A N = ..! Ac. Biet SAoN 60cm2• Tfn h SAsc. = 3 c B Bai 1 24. L u c 6 g i O', m<)t x e t3 i di t u A den B v6'i v� n toe 40k m/h . L u c 7 g i a 30 phut, --� - � m <)t xe du l i ch di tu B ve A vdi v� n toe S O km/h . B iet qua n g duang A B dai 270 k m . H o i h a i x e g � p n h a u l uc m·ay g i o? B a i 33. Tam g ia c A BC c6 d i $ n t fch 280c m2. Lay diem M c9 n h A B sao cho AM = M B . B h ? m N tnen c� n h s a o c h o B N = _! NC; A N cat C M ta i. 3 diem L d i�n tfch tu g i a c 1 H a l xe kh 6i h a n h cu n g luc ve p h fa n h a u . MQt xe tu A, m <)t xe di B . Sau B 1 g i o 3 0 p h ut xe e a c h Tfn h quang ABf b i et x e ca q u it n g du'o n g m at 6 g iO', xe ca q ua n g duO'ng B A mat 5 g Rise a nd
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A RC H I M ED ES SC H OO L Toa n s - Q u y en 3 . 1 C . Ch uyen d9ng n g u'9'c c h i eu g�p n h a u --- ----- --- ----- -- -------· Cac b a i to a h ch uyen a¢ng de u c o 2 v :1 t u yen a¢ n g khoi h a n h c u n g l lJ c ----- ---- - - - -- - - ----- - - -- - - ' ------- ---- -- ------�-------- -�------------�-- ---------- ---- G 9 i kh o a n g cac h b a n da u Ia S H a i v�t ch uyen oc)n g aeu n g uqc chieu n h a u v6i v � n toc V 1 va V 2 , xuat phat cung m9t luc v a .) each n h au m ¢t 009 n s th1 t h a i g i a n t de h a i ch uyen a(; n g g�p n hau 1.3 : Bai 34. C h o ta m g i a c ABC, f\1 1 a di em c h ln h g i U'a cua c9 n h BC, N tren c9 n h AC s a o .cho CN 3AN. MN keo d a i cat B A keo d a i t� i E. Tfn h di$n tfch ta m g i a c A N E/ biet di�n t i c h = ta m g i a c ABC ba n g 2 1 6 c m 2 . B f d 1 1 9 . Hai tha n h ph 6 A va B e a c h_ n h a u 400km. Lu c 1 Oh sa n g , m9t g a n may di t u x e A aen B voi v�n t6c 3 5 km/h v a m (>t x e d u lfch a i tu B v e A v6i v � n toe 1 1 5 km /h . Ho i 2 xe g�p n hau I CJ C m ay gi b? Bai 1 20.. Hai tinh AB each nhau 1 50km, H a i 6 t6 cung khoi h a n h l uc 7 g i a 30 p h ut de di tu A den B va tu B den A. Hoi den may g io thl h a i xe g � p n ha u , biet v� n toe cua hai x e Ian h lQ't I a 5 5km/h va 65 km/h? flif�m g�p nhau each A bao n h ieu ki-16..,m et? Bai 35. C h o tam g ia c ABC c6 d i �n tfch 1 56cm 2• E Ia A di em c h fn h gicra BC. Tren do<?n AE lay diem I chfnh g i ua . Noi B ! keo d a i cat A C a D . Tfnh d i�n tfch ta m g ia t A ID. Bai 1 21 . Hai thanh ph6 A, B each nhau 2 1 4km. Cu n g l uc, mqt xe g a n may ai tU' A den B va m¢t xe du l jch di tu B ve A. Sau 2 g ial h9 g � p n ha u Ci diem C each A 84km. Tfn h v�n toe cua m-6i xe. and g ra s pRise a b ovethe worldoneself A rchi m ed es SchoolAschooi .ed u.vn I 5 5
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� . l i d \; r 1 n 6 d u n h B · I a b a o, t h a n g Ia hl n h t v g i i K co G;) n h a6i so n g H a i c 9 n h s o n g s o n g g Q i I a c9 n h da y (day 1Cin1 da y b e ) . ------ --- - --·----- ··� .�.·----· -- � H a i c� n h c o n l�i g Q i I a h a i G? n h ben . D H - Ch i e u ca o hl n h th a n g 1. 3 do � n t ha n g vu6ng g6c v6i 2 C9 n h day c u a hln h t h a n g . - Hl n h t h a n g ABCD c6 2 c� n h day Ia A B va D C, h a i c9 n h ben Ia AD va BC. AH L3 avong Bai 1 1 M¢t n g u'O'i di xe m a y tu dja cli em A den B de h Qp. N eu n g lioi ay di voi v�n c a o hl n h th a n g ABCD. t6c 25 km/h thl den B c h � m 2 g i c'J. N eu di voi v� n toe 30km/h t hl den B ch�m 1 g i O'. Hoi Cac d�ng hln h q u a n g auan g A B d a i bao nhieu ki-lo-met? Hl n h t h a n g th uong Bai 1 1 8. M¢t 6 to ai tu A den 81 n e u di vai v�n toe SOkm/h thl aen 8 c h � m mat 2 g io 8 A so v6i d lf al nh. Neu di v6i toe 60km/h thl den B s6m h n g iG' so vai d lf d!n h . 8 v� n a 1 r----··---�.., Tfn h q ua n g auong AB. c 0 tha n g vu o n g Hl n h th a n g (co m9t cqnh ben vu6ng g6c (c6 hai cgnh nhau) voi hai Rise a bove o n eself
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A RC H I M E D ES SC H OOL Toa n s - Q uyen 3 . 1 3 . Di�n t ic h hi n h t h a n g . Ba i 1 1 3 . Qu a ng a uo n g A B d a i 1 0 3 km . Lu c 8 gic 1 5 o h ut, m¢t 6 t o en t u A den B vdi 5 d i �n tfc h; d9 cac c� n h da y; v�n toe SOkm/h. f) j O IJCJC 40 knl , xe h 6 ng s Lta mat 45 p tl ut. Q u a ng au'dng co n f � L xe chi I a a , b I a d a i B A .J h Ia c h i e u 1J'n g . C h <? Y v 6i v� ri toe 45 km/h . H o i x e aen- 8 I lK m ay g io? c a o t uo n q � �- - ---� ! . ··--..,\ / I ' r (a + b) x h / i .J = I h . '.\. 2 i I I \\, a + b = S x 2 / I \.'· / '\...,�. h _t1 . . .":::. _ c h = S x 2 [) H b a + b (a, b, h c u n g dan vj do) . . % . Bai 1 1 4. M9t xe m a y di tv A den B voi v3.n toe 35 km/h va kh i q u ay ve A voi v? n toe Vi dt,J 1 : MQt mim h dilt hln h thang c6 ctay n h 6 3 0 m , ctay I On b a n g day rlhO. Chh�u 25km/h. Tfn h quang auong tli A den B biet thai gian ca ai L3n ve Ia 4 g i a 48 p hut. c a o bang tfu ng bl nh c¢ng cua h a i day. a) Tlnh di�n tich ma n h oat a6. b) N g uoi ta su d t} n g 30% di�n tfch de tro n g n g of 50% di�n tkh de tr6 n g khoai, di�n tfch co n l 9 i tron g ra u. Tfn h d i� n tfch trong ng6, d i�n tfch tr6ng khoa i, tro ng rau� Bai lam a) Day ICinm a n h dat Ia: 30 : 3 x 5 SO(m) = Ch ieu ca o manh dat Ia: (50 + 30) : 2 = 40(m) Di�n tfch man h dat Ia: (50 + 30) X 40 : 2 1 600(m2) = b) Di�n tfch tr6ng ng6 Ia: 1 600 x 30°/o 480 (m2) = Di�n tfch tr6ng khoai Ia: 1 600 sog'o= 800(m2) X 1 600 - 480 - B a i 1 1 5. fv19t o to di tu A den B m at 4 gio. Neu 6 t6 ta ng v� n toe the m 14km/h thl di Di� n tfch tro n g rau I a : soo = 3 20(m2) 1 600m2; 2 tli A den B chi mat 3 g i O'. Tfn h q u a n g au'ong A B . f)ap s6: 480 m2; 800 m2; 3 20 m Vi d l} 2: M¢t m a n h dat hl n h tha n g c6 di�n tkh Ia 357m2• Sau kh i mo r¢ng c1ay n h6 them 3 m va day ion them S m thl di?n t fch ta ng t hem 48 m2• Tlnh d9 dai moi da y cua manh dat bh�t ban dau day !on han day n h6 Ia 8,8m. Bai lam Chieu cao hl n h thang Ia: 48 x 2 : ( 3 + 5) 1 2(m) = Tong day nh6 va day lon f a : 357 X 2 : 1 2 = 5 9/S (m) Day nh6 I a : (59,5 - 8,8) : 2 =25,3 5 (m) Day Ian l�t 59,5 - 25,35 34,1 5 (m) = Bap so: 25,3 5 m; 24,1 5 m Rise a bove o n eself Archi medes School I 5 3 a nd g rasp the world Asch ool .ed u.vn
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rn ; n C d O n A 8 j 1 1 ______, ______ __________ , _ _,__ q u a ng dLJb n g A B d a i n g tJO'i t Cr A m ay g i d, b iet d 9c� alfO' n g cl6 m at 3 0 ----'------ --------------·--' ·'--·------- M (>t hl n h tha ng c6 day Ian d a i 8 1 e m , day b e b a n g � day Ia n, c h ie u cao b a n g 9 _i_ aay be. Tfn h d ien tfch hl n h. t h a ng. 1 0 B a i 1 1 1 . Tren q u a ng duong A B, m 9t xe m ay di v6'i v�n toe 44km/h thl m at 2 g i o 30 phut. M<)t 6 to di voi v�n toe gap nJO'i xe may thl mat bao lau? B iJ i 38. M<?t kh u dat hlnh tha n g co day n ho bang 1 2,4m; day nh6 ba n g nU'a day 16'n va kem ehieu cao 1 ,2 5 m . Tfn h di�n tlch kh u oat d6. B ai 1 1 2 4 Qua n g dVO'ng AB dai 1 77 k m . Luc - 7 gid, T u ctl xe m ay tU' A den B . T u di 2 gio dau v6'i v� n toc 3 6 km/h . f) o � n dvang con l � i Tu tan g v� n toe them 9 k m m o i g i a. Ho i T u den B l uc may g i o? B a i M9t hl n h t h a n g c 6 tong a<? dai h a i day I a 42 c m Neu m o r<? n g day be t h em . S c m thl di$n tfc h h l n h tha n g se ta n g th e m I a 30cm2• Tin h d i � n tfc h h l n h th a n g .
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A RC H I M EDES SC H O O L Toan s Q uyen 3 . 1 - B a i 40. M 9 t m a n h dat hl n h tha n g c6 t o n g h a i da y I a 49 rn . N e u t h e m vao day b e 4, 5 m B. Cac b id toa n v e chuyen d{>ng dO'n v a th e m va o day i 6n 1 2 1 5 m t h l di�n tfc h m a n h dat s e t a n g l e n 1 44, 5 m2 • Tin h d i � n t fd1 khoi h a n h B a i 1 06 . Xe m a y tu A l u c 5 g io 45 p h u t va di den 8 l uc 7 g i 0 v6'i v� n toe m a n h oat hl n h t h a n g i u c aa u , 4 0 k rn/g i o . T l n h q u a n g avan g A B . ----·-- -------- ----------- -- - - - -- ------- B a i 1 0 1 . L u c 7 g i a 20 phut, m9t n g uai d i x e d9 p vdi v� n toe 1 2km/g io a i tu A den B . Biet q u a n g duo n g AB dai 1 8km . Hoi n g ubi ay den B l uc may gio? Bai 41 . M¢t thua ru¢ng hrnh tha n g c6 trung bl n h c¢ng cua hai day Ia 6 0 m, duon g cao ba n g c� n h cua m ¢t hl n h vuon g c6 c h u vi 1 60m. N g uCil ta cay lua tn?n thua ru ¢ng nay/ cu 300m2 thu duqc 3,5 t� th6c. Tfn h xem ca thU'a ru9ng thu du'qc bao n h i e u tan t h 6c. Bili 1 0s . M{>t oto khoi h a n h tv A l u c 7 g i a, den B l u c 1 1 g i o 45 phut. G i ua dvang xe n g h i 30 p h ut. Tfnh v�n toe cua 6 t6 biet q u a n g dvang AB d a i 1 70km. hlnh � Bai 42. fv1(>t manh vvon tha n g vuong c6 day be bang aay 16'n . Neu keo dEli aay be them 30m n va thl hl nh tha n g trb tha n h hl nh ch u nh�t va di$n tfch ta ng them 675 m2• Tfn h dl$n t fch man h vu'on do. Bai 1 09. A n h N a m di c6ng tac o tru ng ta m Hai Phong bang xe may, a n h k h oi ha nh l uc 1 1 g io 1 5 phut v6'i v�n toe 36km/h. A n h den n ai l uc 1 5 g i o 45 p h ut Tren auong di . a n h d ung l<;ti nghl h et 1 g io 1 0 ph ut. Hoi tU' nha a n h den tru n g tam H ai P h o n g each bao nhieu ki-16-met? R ise a bove o nese lf Arch i m edes Sch ool I 5 1 and grasp the world Asc h oo l .ed u.vn
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