Question

Question 8
If $\Delta ABC\sim \Delta PQR,and\frac{BC}{QR}=\frac{1}{3},then\frac{ar\left(\Delta PRQ\right)}{ar\left(\Delta BCA\right)}$ is equal to

(A) 9
(B) 3
(C) $\frac{1}{3}$
(D) $\frac{1}{9}$

Answer 1

(A) 9

Given $\Delta ABC\sim \Delta PQR,and\frac{BC}{QR}=\frac{1}{3}$
We know that the ratio of the areas of two similar triangles is equal to square of the ratio of their corresponding sides.
$\therefore$ $\frac{ar\left(\Delta PRQ\right)}{ar\left(\Delta BCA\right)}=\frac{(QR{)}^2}{(BC{)}^2}={\left(\frac{QR}{BC}\right)}^2={\left(\frac{3}{1}\right)}^2=\frac{9}{1}=9$