Question:
It is given that $\Delta A B C \sim \Delta P Q R$ and $\frac{B C}{Q R}=\frac{2}{3}$, then $\frac{\operatorname{ar}(\Delta P Q R)}{\operatorname{ar}(\Delta A B C)}=?$
(a) $\frac{2}{3}$
(b) $\frac{3}{2}$
(c) $\frac{4}{9}$
(d) $\frac{9}{4}$
Solution:
(d) 9 : 4
It is given that $\Delta A B C \sim \Delta P Q R$ and $\frac{B C}{Q R}=\frac{2}{3}$.
Therefore,
$\frac{\operatorname{ar}(\triangle P Q R)}{\operatorname{ar}(\triangle A B C)}=\frac{Q R^{2}}{B C^{2}}=\left(\frac{3}{2}\right)^{2}=\frac{9}{4}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.