Question

∆ABC ~ ∆PQR and their areas are in the ratio 25 : 9. If BC = 5cm, the length
of QR is
A. 8 cm
B. 3 cm
C. 3.5 cm
D. 9 cm​

Answer 1

Step-by-step explanation:

Area(∆ABC)=BC²/

Area(∆PQR)=QR²

25/9=5²/QR²

5/3=5/QR

5QR=15

QR=15/5

QR=3cm

Answer 2

The length of QR is B) 3cm.

Step-by-step explanation:

Given:

∆ABC ~ ∆PQR, ratio of their areas= 25:9, BC=5cm

To find:

length of QR

Solution:

The length BC is the base of ∆ABC & length QR is the base of ∆PQR

It is given that triangles ABC & PQR are similar

∴ The ratios of their areas will be equal to their square of bases and in proportion

Symbolically,

A(ABC) = BC²

A(PQR)     QR²

∴ 25 = (5)²

   9      QR²

∴ 25 = 25

   9      QR²

∴ 25 X QR²= 25 X 9

∴ 25 X QR²= 225

∴ QR²= 225/25

∴ QR²= 9

∴ QR = √9

∴ QR = ±3

But the length cannot be negative, hence the length of QR= 3cm.

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