If the areas of two similar triangles ABC and PQR are in the ratio 9 : 16 and BC = 4.5 cm,
Question:

If the areas of two similar triangles ABC and PQR are in the ratio 9 : 16 and BC = 4.5 cm, what is the length of QR?

Solution:

Given:  ΔABC and ΔPQR are similar triangles. Area of ΔABC: Area of ΔPQR = 9:16 and BC = 4.5cm.

To find: Length of QR

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

Hence,

$\frac{\operatorname{ar}(\Delta \mathrm{ABC})}{\operatorname{ar}(\Delta \mathrm{PQR})}=\frac{\mathrm{BC}^{2}}{\mathrm{QR}^{2}}$

$\frac{9}{16}=\frac{4.5^{2}}{Q R^{2}}$

$\mathrm{QR}^{2}=\frac{4.5^{2} \times 16}{9}$

$\mathrm{QR}^{2}=36$

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