Question

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

Answer 1

$\Delta ABC\sim \Delta PQR$

$ar\left(\Delta ABC\right)=4ar\left(\Delta PQR\right)$

$\frac{area\Delta ABC}{area\Delta PQR}=\frac{4}{1}$

$\frac{area\left(\Delta ABC\right)}{area\left(\Delta PQR\right)}=\frac{B{C}^2}{Q{R}^2}$

$\frac{4}{1}=\frac{B{C}^2}{Q{R}^2}$

$\Rightarrow {\left(\frac{2}{1}\right)}^2={\left(\frac{12}{QR}\right)}^2$

$\frac{2}{1}=\frac{12}{QR}$

$\Rightarrow QR=\frac{12\times 1}{2}=6$

$QR=6cm$