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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Updated on: 10-Oct-2022

"&description=In a 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 proportiona','sharer','toolbar=0,status=0,width=580,height=325');" href="javascript: void(0)" title="Share on Facebook"> "&summary=In a 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 proportiona','sharer','toolbar=0,status=0,width=580,height=325');" href="javascript: void(0)" title="Share on LinkedIn">

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