Question

$\Delta ABC\sim \Delta PQR$. Also, $ar\left(\Delta ABC\right)=4ar\left(\Delta PQR\right)$. If $BC=12cm,$ then find $QR$.

Answer 1

Given: $ar\left(\Delta ABC\right)=4ar\left(\Delta PQR\right)$
$\Rightarrow \frac{ar\left(\Delta ABC\right)}{ar\left(\Delta PQR\right)}=\frac{4}{1}$
$\Rightarrow \frac{B{C}^2}{Q{R}^2}=\frac{4}{1}$
[$\therefore$ The ratio of the areas of two similar $\Delta s$ is equal to the ratio of the squares of any two corresponding sides]
$\Rightarrow \frac{(12{)}^2}{Q{R}^2}=\frac{4}{1}$ [$\therefore$ QR= 12 cm]
$\Rightarrow Q{R}^2=\frac{12\times 12}{4}=36$
$\therefore QR=\sqrt{36}=6cm$