Question

$\Delta ABC$ is similar to $\Delta PQR$, ar($\Delta ABC$) = 36 sq. cm. and ar($\Delta PQR$) =49 sq.cm. If BC = 12 cm, find QR.

Answer 1

$\because \Delta ABC\sim \Delta PQR$
$\therefore \frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}=\frac{B{C}^2}{Q{R}^2}$
$\Rightarrow \frac{36}{49}=\frac{{12}^2}{Q{R}^2}$
$\Rightarrow (QR{)}^2=\frac{12\times 12\times 49}{36}=4\times 49$
$\Rightarrow QR=+\sqrt{4\times 49}$
$=2\times 7=14cm$