Question

The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, find the length of QR.

Answer 1

SOLUTION :

Given: ΔABC∼ΔPQR , arΔABC : arΔPQR =  9:16 and BC = 4.5cm.

We know that the ratio of the areas of the two similar triangles is equal to the ratio of the squares of their corresponding sides.

arΔABC/arΔPQR = (BC/QR)²

9/16 = (4.5/QR)2

√9/16 = (4.5/QR)

¾ = 4.5/QR

3 × QR = 4.5 × 4

QR = (4.5× 4)/3

QR = 1.5 × 4  

QR = 6 cm

Hence, the length of QR is 6 cm.

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Answer 2

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