Question

If $△ABC\sim △PQR,$ $\frac{ar\left(ABC\right)}{ar\left(PQR\right)}=\frac{9}{4}$, $AB=18$ $cm$ and $BC=15$ $cm$, then $QR$ is equal to:

• A. $10$ $cm$
• B. $12$ $cm$
• C. $\frac{20}{3}$ $cm$
• D. $8$ $cm$

Answer 1

The correct option is A $10$ $cm$

Given, $△ABC\sim △PQR$,

Then, $\frac{ar\left(ABC\right)}{ar\left(PQR\right)}=\frac{A{B}^2}{P{Q}^2}=\frac{B{C}^2}{Q{R}^2}=\frac{A{C}^2}{P{R}^2}$

$\frac{9}{4}=\frac{B{C}^2}{Q{R}^2}$

$\frac{9}{4}=\frac{{15}^2}{Q{R}^2}$

$Q{R}^2=\frac{4\times 225}{9}$

$Q{R}^2=100$
$QR=10cm$