In a $Δ$ ABC, D and E are points on the sides AB and AC respectively such that DE $||$ BC.If AD $=$ 6 cm, DB $=$ 9 cm and AE $=$ 8 cm, find AC.
Given:
In a $Δ$ ABC, D and E are points on the sides AB and AC respectively such that DE $||$ BC.
AD $=$ 6 cm, DB $=$ 9 cm and AE $=$ 8 cm.
To do:
We have to find the value of AC.
Solution:
DE $||$ BC (given)
Therefore,
By Basic proportionality theorem,
$\frac{AD}{DB}=\frac{AE}{EC}$
$ \begin{array}{l}
\frac{6}{9} =\frac{8}{EC}\\
\\
EC=\frac{8\times 9}{6}\\
\\
EC=\frac{72}{6}\\
\\
EC=12\ cm
\end{array}$
From the figure,
$AC=AE+EC$
$AC=(8+12) cm$
$AC=20 cm$
The measure of $AC$ is $20 cm$.
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