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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 $AD\ =\ 2.5\ cm$, $BD\ =\ 3.0\ cm$, 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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