Question

A triangle A′BC′ is constructed similar to $\Delta ABC$ with a scale factor $\frac{3}{4}$, then the ratio of areas of $\Delta A\text{'}BC\text{'}and\Delta ABC$ will be

• A. 3:2
• B. 9:16
• C. 6:5
• D. 3:1

Answer 1

The correct option is B 9:16

Given:$\Delta P^{\prime }Q{R}^{\prime }\sim \Delta PQR$
$\therefore \frac{Area\left(\Delta P^{\prime }Q{R}^{\prime }\right)}{Area\left(\Delta PQR\right)}=(\text{Ratio of corresponding sides}{)}^2$
$={\left(\frac{3}{4}\right)}^2(\because Scalefactor=\frac{3}{4})$
$=\frac{9}{16}$

$\Rightarrow Area\left(\Delta P^{\prime }QR\right):Area\left(\Delta ABC\right)=9:16$

Hence, the correct answer is option b.