Question

In the figure $BC=2$ then $DE=$____.

• A. $4cm$
• B. $5cm$
• C. $6cm$
• D. $noneofthese$

Answer 1

Answer: (B)

From figure, $\frac{AB}{AD}=\frac{2.4}{6}=\frac{24}{60}=\frac{4}{10}=\frac{2}{5}-\left(1\right)$

$\frac{AC}{AE}=\frac{3.2}{80}=\frac{4}{10}=\frac{2}{5}-\left(2\right)$

In $\Delta ABC$ and $\Delta ADE$

$\frac{AB}{AD}=\frac{AC}{AE}\left(from1\&2\right)$

$\angle A=\angle A\left(common\right)$

$\Delta ABC\sim \Delta ADE$

$\Rightarrow \frac{BC}{DE}=\frac{AB}{AD}$

$\Rightarrow \frac{2}{DE}=\frac{2.4}{60}=\frac{2}{5}$

$\Rightarrow \frac{2}{DE}=\frac{2}{5}$

$\Rightarrow DE=5cm$