Question

It is given that ∆ ABC ∼ ∆PQR and $\frac{BC}{QR}=\frac{2}{3},\mathrm{then}\frac{\mathrm{ar}(∆PQR)}{\mathrm{ar}(∆ABC)}=?$
(a) $\frac{2}{3}$
(b) $\frac{3}{2}$
(c) $\frac{4}{9}$
(d) $\frac{9}{4}$

Answer 1

(d) 9 : 4
It is given that ∆ ABC ∼ ∆PQR and $\frac{BC}{QR}=\frac{2}{3}$.
Therefore,
$\frac{ar(△PQR)}{ar(△ABC)}=\frac{Q{R}^2}{B{C}^2}={\left(\frac{3}{2}\right)}^2=\frac{9}{4}$