Question

In a $\Delta ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE||BC$.
If $AD=2cm,AB=6cm$ and $AC=9cm$, find $AE$.

Answer 1

$\begin{array}{c}AD=2cmAB=6cmAC=9cm.\\ In\Delta ADE\&\Delta ABC\\ \angle A=\angle A\&\angle ADE=\angle ABC\\ \therefore \Delta ADE\sim \Delta ABC\left(AAsimilarity\right)\\ \therefore \frac{AD}{AB}=\frac{AE}{AC}\\ \Rightarrow \frac{2}{6}=\frac{AE}{9}\\ \therefore AE=\frac{9\times 2}{6}=3cm.\end{array}$