Question

If $△ABC\sim △ADE$ and ar $(△ADE)$ = 9 ar $(△ABC)$ then $\frac{BC}{DE}$ is equal to

• A. $\frac{1}{3}$
• B. $\frac{1}{9}$
• C. $\frac{3}{4}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{3}$

From question,
$ar\left(\Delta ADE\right)=9ar\left(\Delta ABC\right)$

or $\frac{ar\left(\Delta ABC\right)}{ar\left(\Delta ADE\right)}=\frac{1}{9}=\frac{B{C}^2}{D{E}^2}$

Hence $\frac{BC}{DE}=\sqrt{\frac{1}{9}}=\frac{1}{3}$