Question

The areas of two similar triangles ABC and PQR are 64 cm${}^2$ and 121 cm${}^2$, respectively. If QR = 15.4 cm, find BC.

Answer 1

We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
$\therefore \frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}=\frac{B{C}^2}{Q{R}^2}\Rightarrow \frac{64}{121}=\frac{B{C}^2}{(15.4{)}^2}$

$\Rightarrow \frac{8}{11}=\frac{BC}{15.4}$

$\Rightarrow BC=\frac{8\times 15.4}{11}=11.2cm$