In a $Δ\ ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\ ||\ BC$.
If $AD\ =\ 4\ cm$, $DB\ =\ 4.5\ cm$ and $AE\ =\ 8\ cm$, find $AC$.

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Given:

In a $Δ$ ABC, D and E are points on the sides AB and AC respectively such that DE $||$ BC.

AD $=$ 4 cm, DB $=$ 4.5 cm and AE $=$ 8 cm.

To do:

We have to find the value of AC.

Solution:

DE $||$ BC (given)

Therefore,

By Basic proportionality theorem,

$\frac{AD}{DB}=\frac{AE}{EC}$

$\frac{4}{4.5} =\frac{8}{EC}$

$EC=\frac{8\times 4.5}{4}$

$EC=\frac{36}{4}$

$EC=9 cm$

From the figure,

$AC=AE+EC$

$AC=(8+9) cm$

$AC=17 cm$

The measure of $AC$ is $17 cm$.

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Updated on: 10-Oct-2022

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