Question

It is given that $\Delta ABC\sim \Delta PQR$ with $\frac{BC}{QR}=\frac{1}{3}$. Then $\frac{ar\left(\Delta PQR\right)}{ar\left(\Delta ABC\right)}$ is equal to

• A. $9$
• B. $3$
• C. $\frac{1}{3}$
• D. $\frac{1}{9}$

Answer 1

The correct option is A $9$

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Since, $\Delta ABC\sim \Delta PQR$

$\therefore \frac{ar\left(\Delta PQR\right)}{ar\left(\Delta ABC\right)}=\frac{P{R}^2}{A{C}^2}=\frac{Q{R}^2}{B{C}^2}=\frac{9}{1}=9..........[\therefore \frac{QR}{BC}=\frac{3}{1}]$