Question

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

• A. $10cm$
• B. $12cm$
• C. $20cm$
• D. $8cm$

Answer 1

The correct option is A $10cm$

Given $△ABC\sim △QRP$
Therefore, $\frac{Area△ABC}{Area△QRP}=\frac{{BC}^2}{{PR}^2}$
or $\frac{9}{4}=\frac{{15}^2}{{PR}^2}$
or ${PR}^2=\frac{{15}^2\times 4}{9}cm$
Therefore, $PR=\frac{15\times 2}{3}=$ $10cm.$