In a $Δ\ ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\ ||\ BC$.
If $AD\ =\ 2.5\ cm$, $BD\ =\ 3.0\ cm$, and $AE\ =\ 3.75\ cm$, find the length of $AC$.

img src=/doubts_assets/images/158630-1605790744.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 $=$ 2.5 cm, DB $=$ 3 cm and AE $=$ 3.75 cm.

To do:

We have to find the value of AC.

Solution:

DE $||$ BC (given)

Therefore,

By Basic proportionality theorem, $\frac{AD}{DB}=\frac{AE}{EC}$

$\frac{2.5}{3} =\frac{3.75}{EC}$

$EC=\frac{3.75\times 3}{2.5}$

$EC=\frac{11.25}{2.5}$

$EC=4.5 cm$

From the figure,

$AC=AE+EC$

$AC=(3.75+4.5) cm$

$AC=8.25 cm$

The measure of $AC$ is $8.25 cm$.   

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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 2 5 cm BD 3 0 cm and AE 3 75 cm find the length of AC img src doubts assets images 158630 1605790744 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 $=$ 2.5 cm, DB $=$ 3 cm and AE $=$ 3.75 cm.To do:We have to find the value of AC.Solution:DE $||$ BC (given)Therefore,By Basic proportionality theorem, $frac{AD}{DB}=frac{AE}{EC}$$frac{2.5}{3} =fr','sharer','toolbar=0,status=0,width=580,height=325');" href="javascript: void(0)" title="Share on Facebook"> "&summary=In a ABC D and E are points on the sides AB and AC respectively such that DE BC If AD 2 5 cm BD 3 0 cm and AE 3 75 cm find the length of AC img src doubts assets images 158630 1605790744 png style width 25 - Given:In a $Δ$ ABC, D and E are points on the sides AB and AC respectively such that DE $||$ BC.AD $=$ 2.5 cm, DB $=$ 3 cm and AE $=$ 3.75 cm.To do:We have to find the value of AC.Solution:DE $||$ BC (given)Therefore,By Basic proportionality theorem, $frac{AD}{DB}=frac{AE}{EC}$$frac{2.5}{3} =fr','sharer','toolbar=0,status=0,width=580,height=325');" href="javascript: void(0)" title="Share on LinkedIn">

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