Question

In the figure, $BC\parallel DE$ and $\frac{AB}{AD}=\frac{3}{4}$
What is the ratio between the area of $△ABC$ and $△ADE$?

• A. $\frac{3}{4}$
• B. $\frac{9}{32}$
• C. $\frac{3}{8}$
• D. $\frac{9}{16}$
• E. $\frac{8}{9}$

Answer 1

The correct option is D $\frac{9}{16}$

GIven: $BC\parallel DE$ & $\frac{AB}{AD}=\frac{3}{4}$

In $△ABC$ & $△ADE$

$△ABC\sim △ADE$ (by $AAA$ property)

$\therefore {\left(\frac{AB}{AD}\right)}^2=\frac{area\left(ABC\right)}{area\left(ADE\right)}$

$\frac{area\left(ABC\right)}{area\left(ADE\right)}=\frac{9}{16}$