Question

In $△ABC$, $D$ and $E$ are points on $AB$ and $AC$ respectively such that $DE\parallel BC$. If $AE=2cm,EC=3cm$ and $BC=10cm$, then $DE$ is equal to:

• A. $5cm$
• B. $4cm$
• C. $15cm$
• D. $\frac{20}{3}cm$

Answer 1

The correct option is B $4cm$

In $△ABC$, $DE$ is parallel to $BC$

Thus, $DE$ divides the two sides $AB$ and $AC$ proportionally.

Thus,

$\frac{AD}{AB}=\frac{AE}{AC}$

Thus, $△ABC\sim △ADE$

$\frac{AB}{AD}=\frac{AC}{AE}=\frac{BC}{DE}$ [C.S.C.T.]

Now,

$\frac{AC}{AE}=\frac{BC}{DE}$

$\Rightarrow DE=\frac{AE\times BC}{AC}$

$\Rightarrow DE=\frac{2\times 10}{5}$ [ $\because AC=(AE+EC)=2+3=5$]

$\Rightarrow DE=4$ cm