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 $4 cm$.

Tutorialspoint

Updated on: 10-Oct-2022

36 Views

Kickstart Your Career

Get certified by completing the course

Get Started