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
$\frac{9}{16}=\left(\frac{4.5}{Q R}\right)^{2}$
$\frac{3}{4}=\frac{4.5}{Q R}$
$\mathrm{QR}=\frac{4 \times 4.5}{3}$
$Q R=6 \mathrm{~cm}$