1. Trójkąt A`B`C` jest podobny do trójkąta ABC. Oblicz skalę podobieństwa oraz długości boków B`C` i.... Question from @klaudiaaa

poziomka777 1]
B prim C prim=x
A prim C prim =y

k=6:20=0,3
x=x:25=0,3
x=25×0,3
x=7,5cm

y=y:30=0,3
y=30×0,3=9cm
2]
x=wzrost chłopca
z talesa:
1,5:x=(0,5+1,5):2,4
2x=2,4×1,5
2x=3,6
x=3,6:2
x=1,8m
odp. chłopiec ma wzrostu 1,8m

1 votes Thanks 2

ata45 Trójkąty są podobne, gdy stosunki odpowiednich boków są równe:
A'B'/AB=B'C'/BC=C'A'/CA

/ - kreska ułamkowa

z danych zadania znamy dł, AB i A'B'
obliczam skalę podobieństwa:
A'B'/AB=6cm/20cm=3/10

Obliczam B'C':
B'C'/25cm=3/10 /*25cm (obie strony mnożę przez 25cm)
B'C'=3/10*25cm=15/2cm=7,5cm
B'C'=7,5cm

Obliczam A'C'
A'C'/30cm=3/10 /*30cm
A'C'=3/10*30cm
A'C'=9cm

Zad. 2
cień latarni = 2m

x/1,5=2,4/2
2x=2,4 * 1,5
2x==3,6
x=1,8

Odp. Zbyszek ma 1,8m wzrostu.

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