In a $Δ\ ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\ ||\ BC$. If $AD\ =\ 8\ cm$, $AB\ =\ 12\ cm$ and $AE\ =\ 12\ cm$, find $CE$.
img src=/doubts_assets/images/158630-1605775434.png" style="width: 25%;">"
Given:
In a $Δ\ ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\ ||\ BC$.
$AD\ =\ 8\ cm$, $AB\ =\ 12\ cm$ and $AE\ =\ 12\ cm$.
To do:
We have to find the measure of $CE$.
Solution:
$DE\ ||\ BC$ (given)
$AB=AD+DB$
$DB=AB-AD=(12-8) cm$
$DB=4 cm$
Therefore,
By Basic proportionality theorem,
$ \begin{array}{l} \frac{AD}{DB} =\frac{AE}{EC}\\ \\ \frac{8}{4} =\frac{12}{EC}\\ \\ EC=\frac{12\times 4}{8}\\ \\ EC=6\ cm \end{array}$
The measure of $CE$ is $6 cm$.
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