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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 $AE$.
"
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,
$\frac{DB}{AD}\ =\ \frac{EC}{AE}$
Adding $1$ on both sides,
$\frac{DB}{AD} + 1 = \frac{EC}{AE} + 1$
$\frac{DB+AD}{AD}=\frac{EC+AE}{AE}$
$\frac{AB}{AD}=\frac{AC}{AE}$
$\frac{6}{2}=\frac{9}{AE}$
$AE=\frac{9}{3}$
$AE=3 cm$
The measure of $AE$ is $3 cm$.
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