Question

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

Answer 1

The ratio of the areas of the similar triangle are in the ratio of the square of the corresponding sides

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

$\frac{4\Delta PQR}{PQR}=\frac{(12{)}^2}{Q{R}^2}$

$(ar\Delta ABC=4ar\Delta PQRandBC=12cmgiven)$

$4=\frac{144}{Q{R}^2}$

$Q{R}^2=\frac{144}{4}$

$Q{R}^2=36$

$QR=\sqrt{36}cm$

$QR=6cm$