In a $Δ\ ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\ ||\ BC$. If $AD\ =\ x\ cm$, $DB\ =\ x\ –\ 2\ cm$, $AE\ =\ x\ +\ 2\ cm$, and $EC\ =\ x\ –\ 1\ cm$, find the value of $x$. "
 Given:
In a $Δ\ ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE\ ||\ BC$.
$AD\ =\ x\ cm$, $AE = x -2 cm$, $DB\ =\ x\ +\ 2\ cm$ and $EC\ =\ x\ –\ 1$.
To do:
We have to find the value of $x$.
Solution:
$DE\ ||\ BC$ (given)
Therefore,
By Basic proportionality theorem,
$\frac{AD}{DB}\ =\ \frac{AE}{EC}$
$ \begin{array}{l} \frac{x}{x-2} =\frac{x+2}{x-1}\\ \\ x( x-1) =( x-2)( x+2)\\ \\ x^{2} -x=x^{2} -4\\ \\ x=4\ cm \end{array}$
The value of $x$ is $4 cm$.
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