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.

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.

Solution:

Given: The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. BC = 4.5cm.

To find: length of QR

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

ar∆ABCar∆PQR=BCQR2

$\frac{9}{16}=\left(\frac{4.5}{Q R}\right)^{2}$

$\frac{3}{4}=\frac{4.5}{Q R}$

$\mathrm{QR}=\frac{4 \times 4.5}{3}$

$Q R=6 \mathrm{~cm}$