Question

In the figure, $△ABC$ is right angled at $B$. $D$ is any point on $AB$. $segDE\perp sideAC$. If $AD=6cm,AB=12cmAC=18cm$. Find $AE$.

• A. $5cm$
• B. $3cm$
• C. $4cm$
• D. $6cm$

Answer 1

The correct option is C $4cm$

In $△ABC$ and $△ADE$,

$\angle BAC=\angle DAE$ (Common angle)

$\angle ABC=\angle AED$ (Each ${90}^{\circ }$)

$\angle ACB=\angle ADE$ (Third angle)

Thus, $△ADE\sim △ABC$ (AAA rule)

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

$\Rightarrow \frac{6}{18}=\frac{AE}{12}$

$\Rightarrow AE=\frac{6\times 12}{18}$

$\Rightarrow AE=4$

Hence, $AE=4cm$