In a $Δ\ ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\ ||\ BC$.

If $AD\ =\ 2\ cm$, $AB\ =\ 6\ cm$ and $AC\ =\ 9\ cm$, find $AE$.

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 Given:

In a $Δ\ ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\ ||\ BC$.

$AD\ =\ 2\ cm$, $AB\ =\ 6\ cm$ and $AC\ =\ 9\ cm$.

To do:

We have to find the measure of $AE$.

Solution:

$DE\ ||\ BC$ (given)

Therefore,

By Basic proportionality theorem,

$\frac{AD}{DB}\ =\ \frac{AE}{EC}$

This implies,

$\frac{DB}{AD}\ =\ \frac{EC}{AE}$

 

$\frac{DB+AD}{AD}=\frac{EC+AE}{AE}$

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

$\frac{6}{2}=\frac{9}{AE}$

$AE=\frac{9}{3}$

$AE=3 cm$

The measure of $AE$ is $3 cm$.