toán lớp 5 q3

1 n h rn c 9 n h I a A B , va BC h I a al n h dl nh B, d i n h C • Ba g 6c I a g 6 c dl n h A; g 6 c dl n h S; g 6 c al n h C D ucm g c a o c u a ta m g i a c I a OO( l n t h a n g ke t u mot dln h v[.]

1 n h rn

c9 n h I a : AB, va BC

h Ia : aln h dlnh B, din h C

• Ba g6c Ia: g6c dln h A; g6c dln h S; g6c aln h C

Ducmg cao cua ta m giac I a OO(:ln thang ke tu mot

dlnh va vuong goc v6'i c� n h doi di�n (c�nh day)

DQ dai cua dliong cao Ia chieu cao cua ta m giac

M¢t tam giac c6 3 duang cao

2 Tam giac ABC c6:

A H Ia chieu cao tu'ong ung voi c� n h day BC;

Bl la chieu cao tuang ung v6'i c9nh AC;

CK Ia c h ieu cao tuong U'ng v6'i c9 n h AB

3 Ca c d�ng ta m g iac

c

( c6 m¢t g6c vu6ng) (2 cgnh nhau) (3 cc;mh bang nhau)

Aschoo

ARCHIMEDES SCHOOL

I L cA.c o�NG sAt TAP

A Tin h cac yeu to cua tam g ia c

Bai 1 Dien ket qua vao 6 trong (v6i a Ia chieu dai m¢t C9n h cua hl n h ta m giac v a h Ia chieu ca o tlfon g U'ng cua c� nh do)

Rise above oneself

and grasp the world

M <?t thva ru(?ng hl n h ta m giiK v u o n g c6 so do m ¢ t C<;J n h g6c vu6ng Ia 8,4m; s6

ao c9n h g6c vuong con l�i ba ng 75o/o so do c� nh da biet Hoi di�n tich cua thlra

r u ¢ n g ba ng bao nh ieu met vuong?

B a i Tfn h di$n tfc h phan to d� m biet: BM = 9cm; MC = 4 c m va di�n tfch hlnh tam

· giac ABM Ia 27cm2•

B

ARCH I �/1E OES SCHOOL

Bai s M ot h!nh ta m giac c6 c<?n h day b.3ng ?_ chieu cao tuong ung Neu keo dai can h

-Bid 9 Chg m¢t ta m giac ABC vuong a A Neu keo dai AC ve phfa C m9t do9 n CO sao

cho AC = CO = 8cm th1 di�n tfch tang them l 44cm2• Tfnh d9 dai C<? n h AB va di�n tich

tam g L3c Vuong ABC

Bai 1 o Cho tam giac ABC c6 di�n tfch 60cm2, c� n h BC dai 1 Ocm

a) Tinh d<) dai auong cao h a t u A xuong c9nh BC

b) Gqi M Ia trung ait�m cua BC Tfn h d i$n tfch tam giac ABM

c) Gqi N ta trung ctiem cua AC Tln h di�n tfch tarn giac ABN

R ise a bove on eself

and g rasp the world

B a i 1 54 Hi$n g io dong h6 chi dung 1 0 gio Hoi thO'i g i a n ngan nhat de kim giC1 va

kim phut thang han g voi nhau?

Archimedes School

I 67

Aschool.ed u.vn ,

AM = 1 6 (em); BM = 32 (em); NO = 1 2 (em); AN = 24(cm)

SABCD = AB x AD = 48 x 36 = 1 728( cm2 ); SAMN =�xAMxAN = �x16 x 24 = 1 92( cm2)

ARCH I M EDES SCHOOL

Bid 1 2 Tfnh d i�n tfch hl nh tlf giac AECG Biet hl nh

Rise above oneself

and grasp the \Norld

Ba i 1 46 N\¢t xe Iva di q ua n-1¢t c¢ t dien het 20 giayl di q u a m9t c3y c,� u dai 450m het

65 giay Tlnh chieu d a l va v�n toe cu a X P l tJa

�

-Bai 1 47 M¢t doa n tau h6a dai 200m ch�y qua m<)t c3i ham Toa aau vao harn k:c 1 0 gio 48 phut,\ toa cuoi ra kh6i ham luc 1 1 gia Moi giG' ta u ch9y dtifjc 27km ll m ch ieu dai cua ham

B a i 1 48 Mqt 6 to di v&i v�n toe SOkm/h vuqt qua m¢t xe Ilia di cung chieu trong 36

g iay Tfn h chieu dai cua x e hJ'a, bit?t v�n toe cua xe I U'a Ia 40km/h

Archimedes School 1- 65 Aschool.ed u vn

1 MQt n g uoi ai tu A den B gom m9t doq n len doc va m<)t do�n xuong doc

V�n toe khi len doc Ia 3km/h, v�n toe khi xu6ng doc Ia 6km/h Thai gi a n ai· cua ngVO'i

d6 1a 3 g i o 30 p h u t va thoi g ian ve Ia 4 g io Tfn h q u a ng cluong A B

Bai 1 An d i tren-m¢t do9 n dVO'ng A B gam m¢t do (;l n len doc va m 9t do�n xuong ·

doc Th ai gian ca di lan ve Ia 8 gio Biet ra n g len d oc vcri v�n toe 3 km/g io va ai

xuong doc voi v� n toe 7km/ giO' Hoi quang auong AB dai bao n h ieu?

c _) i\BM ,

sAMe = MC = _2 (Ch u n g duan g cao ha tv A den BC)

ARCHI MEDES SCHOOL

Bai toan 3 Cho ta m giac ABC, M tren C C:l n h BC, N tn?n AM

5,.1\BM _; SNBM ::::: CM X ' s ACM -SNCM =? ABN s = - ::::::::;> BM s ABN = -� s

- BM ·S SACN CM .SACN s ACM

Bai toan 4 �ho tu giac ABDC c6 di�n tfch Ia 1 oocm2

(h t n h ve en , 1et - b"' ) b· �' -AH 3 = - � T., an h d "· "' ten ttc h t am grac ,

Chu y.w Hai tam gidc c6 chung cgnh day thJ ti I� di�n tfch bang

ti l? 2 duang cao tuang ung

Rise above oneself

and grasp the wo rld

Bai 1 41 B{tn 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 trung blnh cua An tren quang avong ca di lan ve

Bai 1 42 IY!Qt nguai· ai xe d�p tu A den B Khi kh6'i hanh t<?i A, nguoi d6 c1i voi v�n toe

1 Okm/h, n h ung tu ch fn h giua dvang den B ng uoi d6 di' vc:fi v?n toe 1 5km/h Tfnh v�n toe trung bln h cua ngu'oi d6 tren ca quang duong AB

Arch Aschool.edu.vn imed es School 1 63

1 M 9t ca no di -<uoi dong tu A den B vdi v�n toe sokm/g i a Di ngvqc d o n g tu B

den A v6i v�n toe 40km/gia Biet thai g i a n ai xuoi dong ft hO'n thoi gia n di n g llQ'c

do n g Ia 30 phut? Tfnh d¢ dal quang auong AB

Bai 1 39 M9t ca n6 di xuoi d ong tu A den B tren m ¢t khuc son g mat 3 gia va nguqc

do�g tu B tro ve A mat 5 g ia Tfnh chieu dai kh uc son g d6, biet v�n toe cua dong

nvac Ia 60m/phut

Rise

a

p a)

n1 g

ca n h s a :J

b) S CAN =

s CAP - SCPN =

A

c

1 Cho tam g iac ABC, tren c�n h BC lay 3 diem M, N, P sao cho BM = M N = NP =

PC Bietdi�n tkh tam giac AMN Ia 1 2cm2� Tfn h di$n tich tam g iac ABP1 A BC.·

(Chu y: Ve hinh tnroc khi lam bai)

ARCHII\1\EDES SCHC)fJL

sa i 1 s cl·1o

-

····

-

··-· ··· -· · -··

·· ·-··-··-···- · ·· -·

- -·-· ··· · ···- -

AD = DC, BF = FE = EC Tfnh Swc ; Sot:::: ·

- -·

1 �CM, AN = MN Tinh Shew L

-' ··· -··· ··· -·· -

·· -· - _

-· ··-·-· · -···- -�-·

-·-

-· -·· -··-· -·· -·· · ··· · -·

-1 2 I Rise above oneself I and "�rasp the world E Ch uyen d9ng tre n d ong nuoc V • ·Joi :::::: Vthuc + f1tiOC \J ngu'qc :::::: ) "'-nc!f)c = (Vxubi ··· V ngur;rJ : 2 Bai 1 35 L(te 7 gio, rn(lt thuyen may di xubi dong tu ben A den ben B th 6 - I I ' ? S k l A ·" d ' ' i ' 2 2k ' ,

_ uy'- n m a) a -> m!" gto v� n toe on g nU'O'c a , m/g J a t h u ye· n may den B Hoi: a) Th uyen Oldy' den B h.Jc may g io? b) Do dai quang song Ia bao nhh�u kHo-lTlet? - -·· · · -· · ···-··

· ·-·· - _ cua

-··· ··-··· ·· ·· - ;: _ _ ·· -

-

· -· ·· · ···-·· -·

-Bai 1 3 6 V�n toe dong nuoc Ia 1 8 111/ph(1t I\A¢t nguoi bol xuoi quang song dai soorn het 8 phut Hoi ngu'oi o6 bo'i nguqc dong qu��ng song a6 het bao nhieu thO'i gia n? � -

-· -·· -···· -·-· ··-···· ····-·-· -· -·

-·-·-·-··· ·· -· ····-· -·-·-· � - ···

·· -· ·-··· -···-·-··-· · · - -·

Archtmedes School

.

l :t ' Aschool.edu.vn

- - -

- - - - -

Lue 7 g id m9t xe m ay di tv A voi v�n toe 40krn/h Ben 8 giG' 1 5 u t m ¢>t o

to cung �i tu A vO'i v�n toe 60km/h va di cung chieu v6'i xe m ay Hoi den may g id 6 to

duoi k!p xe m ay?

Quang duO'ng AB dai 1 ookm, cung m¢t l uc xe 6 to di tU' A va xe may di tu B

N eu d i ngvqc chieu, hai xe se g?p n hau sau 1 gio 1 5 phut Neu di cung chieu, 6 to

auoi theo xe may thl se g�p nhau sau 5 giO' Tfnh v�n toe xe 6 to, xe m ay

1\RCH I MED ES SCHOOL

I

Bai 24 Cho AM = CM, NB = i'lM, B P ,� � BC , d ien tich

3 tam giae BN P barig 3 crn2 Tin h di�n tfch ta m qiiK ABC

14 1 Rise a b ove o n eself

and grasp the world

Bai 1 30 Hai 6 to 6 A va B each .n h a u 7 S k m c u n q kh oi han h mQt l u c va ai cung chieu

ve p h i a C Sau 2 , 5 g io thl 6 to di tlt A duoi k i p 6 t o di tU' B T1 m v� n toe moi 6 t o bi€t ra.ng tong hat v� n toe I a 1 1 4km/h

Bai 1 3 1 Quang auang AB dai 90 km C6 hai o to cu ng xuat phat n1¢t l uc ?:J A va 6 8,

ai cung chieu ve phfa C Sau 4,5 gio 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 �

4

b) Tfnh quang duong BC

Bai 1 32 M(>t xe may ai tl.r tlnh A den tin h B v6'i v�n toe 45km/gi0' Khi xe may di duqc

1 gia 30 -ph ut thi m¢t 6 t6 di voi v�n t6c 70km/gid tv A auoi thea xe may Biet h a i xe den B cung luc 1 1 gio Hoi :

a) Ttnh A each tlnh B bao nhieu ki l o m et?

b) Xe may da khoi hanh tu A luc may g io?

Arch i med es S chool I 59 Aschool.edu.vn j

s

t = s

1 Lu c 7 g i o, n g udi thv n hat di tv A vdi v�n toe 1 5 km/gi0' Cung t9l B each A

7km, ngvoi th li khoi hanh va di cung ch ieu vdi ngvbi thv n ha't, v6i v�n toe

1 1 km/gio H6i hai ngvoi g�p nhau luc may gio va diem g�p nhau each A bao n h ieu

ki-1 6-met?

Bai 1 29 M¢t 6 to di tu A duoi theo m9t xe may tu B (hai xe cung khoi hanh m<?t luc)

va sau 2,5 gio auoi kip xe may t�i C Stet v�n toe 6 to Ia 65km/gia, v�n toe xe may I a

45 km/gio Tin h q u ang duong AB

27 Cho ta m g iac ABC, tren Ci?nh AB lay dh�m

1v1 sao cho AM = M B; tren cgn h AC· Iay diem N, P

s a o cho AN = N P = PC Tlnh s Asu biet SMNPB = 1 2cm2

(_

A

N

/' /_::, _ _ _ �

ARCH I MEDES SCHOOL·

Bai 3 0 Cho tam g iac ABC Biem M n a m tren AB sao

cho AM = 2MB N Ia trung diem AC f)iem P nam tn§n

BC sao chd BP = 2 BC Tfnh ti le SMNP •

3

SAOC

Rise a bove on eself

and g rasp th e world

-Bai 1 27 (Ams 09 - 70) Cu ng n·1¢t luc nguoi thu nha� ai tu A den B va ngVO'i thu hai d i

tv B a en A, hai nguoi g?p nhau t9i c each A m¢t ao?n 4km Sau d6 nguoi thu nhat di den B roi quay ngay IC?i A ngay, ngu'ai thu hai di den A r6i quay ngay l�i B, hai ngVO'i g�p nhau I an t h u hai t9i D each B m9t do9n 3 km Tfnh a<? dai quang du'Cing A B

Archimed es School I 57 Aschool.edu.vn

1 Luc 6 g ia m (?t xe khach kh oi han h tu A de c:ti den B vO'i v�n toe 60km/h, den

6 g i a 48 phut m<)t xe kh a ch khac khoi hanh tu B di ve A v&i v� n toe 55krn/gio Hai xe

g f? p n ha u l u c 8 gio Tfnh quang dtJC1ng AB

Bai 1 24 Luc 6 giO', m<)t x e t3i di tu A den B v6'i v� n toe 40km/h Luc 7 g i a 30 phut,

m<)t xe du lich di tu B ve A vdi v�n toe SOkm/h B iet qua ng duang AB dai 270km Hoi

ha i x e g�p nhau l uc m·ay g i o?

1 Hal xe kh 6i h a n h cun g luc

1 gio 30 phut xe each

ca quitng du'ong mat 6 g iO', xe

Rise

a nd

ve ph fa n hau MQt xe tu A, m <)t xe di Tfn h quang ABf biet xe

ca q uang duO'ng BA mat 5 g

Bai Cho tam g iac ABC, tren c<?nh B C lay diem M

Ia trung ciiem c9nh BC, diem N nam tren c�n h AC sao cho AN = !Ac Biet SAoN = 60cm2• Tfn h SAsc

3

Bai 33 Tam g iac ABC c6 di$n t fch 280cm2 Lay

diem M c9 n h AB sao cho AM = M B Bh?m N tnen c�nh sao cho B N = _! NC; AN cat C M ta i diem L di�n tfch tu g iac

A RC H I M EDES SCHOOL

- � -��

- - - - - - -

Bai 34 C h o tam g iac ABC, f\1 1a diem chln h g i U'a cua c9 n h BC, N tren c9 n h AC s a o .cho

CN = 3AN MN keo dai cat B A keo d a i t�i E Tfnh di$n tfch tam giac ANE/ biet di�n tich

tam g iac ABC bang 2 1 6cm2

B a i 3 5 Cho tam giac ABC c6 di�n tfch 1 56cm2• E Ia A

diem chfnh gicra BC Tren do<?n AE lay diem I chfnh giua

Noi B! keo dai cat AC a D Tfnh di�n tfch tam g iat AID

Rise above oneself

and grasp the world

Toa n s - Quyen 3 1

C Chuyen d9ng ngu'9'c chieu g�p n h a u Cac bai toah chuyen a¢ng de u c o 2 v:1 t u yen a¢ng khoi h a nh c u n g l lJ c G9i khoang cac'h ban da u Ia S

Hai v�t ch uyen oc)ng aeu nguqc chieu n h a u v6i v�n toc V 1 va V2, xuat phat cung m9t luc va ) each nhau m¢t 009 n s th1 thai gian t de hai ch uyen a(;ng g�p n hau 1.3:

Bfd 1 1 9 Hai thanh ph6 A va B each_ n h a u 400km Lu c 1 Oh sa ng, m9t x e gan may di tu

A aen B voi v�n t6c 3 5 km/h va m(>t x e d u lfch ai tu B ve A v6i v�n toe 1 1 5 km/h Hoi 2

xe g�p nhau I CJC may gi b?

Bai 1 20 Hai tinh AB each nhau 1 50km, Hai 6 t6 cung khoi hanh l uc 7 gia 30 phut de

di tu A den B va tu B den A Hoi den may g io thl hai xe g�p n hau, biet v�n toe cua hai

xe I an hlQ't Ia 55km/h va 65km/h? flif�m g�p nhau each A bao n h ieu ki-16 ,met?

Bai 1 21 Hai thanh ph6 A, B each nhau 21 4km Cung l uc, mqt xe gan may ai tU' A den

B va m¢t xe du ljch di tu B ve A Sau 2 g ial h9 g�p n hau Ci diem C each A 84km Tfnh

v�n toe cua m-6i xe

Archimedes School I 55 Aschooi.edu.vn

i d \; r 1

I a bao,

- - ·- ··� �.··

Bai 1 1 M¢t ngu'O'i di xe may tu dja cli em A den B de hQp Neu nglioi ay di voi v�n

t6c 25 km/h thl den B ch�m 2 g ic'J Neu di voi v�n toe 30km/h thl den B ch�m 1 giO' Hoi

quang auan g AB dai bao nhieu ki-lo-met?

Bai 1 1 8 M¢t 6 to ai tu A den 81 neu di vai v�n toe SOkm/h thl aen 8 ch�m mat 2 g io

so v6i dlf alnh Neu di v6i v� n toe 60km/h thl den B s6m han 1 giG' so vai d lf d!nh

Tfn h q uang auong AB

Rise a bove oneself

t h a n g Ia hl nh tv g iiK co G;) n h a6i son g

� H a i c9 n h s o n g son g g Q i I a c9 n h day (day 1Cin1 day be)

Hai c�n h con l�i gQi I a hai G? n h ben

- Ch i e u ca o hl nh th a n g 1 3 do� n t hang vu6ng g6c v6i 2 C9 n h day cua hln h t h a n g

Vi dt,J 1 : MQt mim h dilt hln h thang c6 ctay nh6 3 0 m , ctay I On bang % day rlhO Chh�u

cao bang tfung blnh c¢ng cua hai day

a) Tlnh di�n tich manh oat a6

b) N g uoi ta su d t} n g 30% di�n tfch de trong ngof 50% di�n tkh de tr6ng khoai, di�n

tfch con l9i trong rau Tfn h d i�n tfch trong ng6, di�n tfch tr6ng khoai, trong rau�

Bai lam a) Day ICin manh dat Ia: 30 : 3 x 5 = SO(m)

Chieu cao 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 X sog'o = 800(m2)

Di�n tfch trong rau Ia: 1 600 - 480 -soo = 320(m2)

f)ap s6: 1 600m2; 480 m2; 800 m2; 320 m2

Vi dl} 2: M¢t manh dat hln h thang c6 di�n tkh Ia 357m2• Sau khi mo r¢ng c1ay nh6

them 3m va day ion them Sm thl di?n tfch ta ng them 48m2• Tlnh d9 dai moi day cua

manh dat bh�t ban dau day !on han day nh6 Ia 8,8m

Bai lam Chieu cao hlnh thang Ia: 48 x 2 : ( 3 + 5) = 1 2(m)

Tong day nh6 va day lon fa: 357 X 2 : 1 2 = 59/S(m)

Day nh6 Ia: (59,5 -8,8) : 2 =25,35(m)

Day I an l�t 59,5 - 25,35 = 34, 1 5 (m)

Bap so: 25,35 m; 24, 1 5 m

Rise above on eself

a nd grasp the world

Toa n s -Quyen 3.1

Ba i 1 1 3 Quang auong A B d a i 1 03km Lu c 8 gic 1 5 o h ut, m¢t 6 to en t u A den B vdi v�n toe SOkm/h f)j OIJCJC 40knl, xe h6ng sLta mat 45 ptl ut Quang au'dng con f�L xe chi Ch<?Y v6i v� ri toe 45km/h Hoi x e aen- 8 I lK may gio?

Bai 1 1 4 M9t xe may di tv A den B voi v3.n toe 35 km/h va khi q u ay ve A voi v?n toe 25km/h Tfnh quang auong tli A den B biet thai gian ca ai L3n ve Ia 4 gia 48 phut

B a i 1 1 5 fv19t o to di tu A den B mat 4 gio Neu 6 t6 tang v�n toe them 14km/h thl di

tli A den B chi mat 3 giO' Tfnh q u a n g au'ong AB

Archimedes School I 53 Aschool.edu.vn