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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 $AD\ =\ 4\ cm$, $AE\ =\ 8\ cm$, $DB\ =\ x\ –\ 4\ cm$ and $EC\ =\ 3x\ –\ 19$, find $x$.

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Academic Mathematics NCERT Class 10

Given:

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

$AD\ =\ 4\ cm$, $AE\ =\ 8\ cm$, $DB\ =\ x\ –\ 4\ cm$ and $EC\ =\ 3x\ –\ 19$.

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{4}{x-4} =\frac{8}{3x-19}\\
\\
4( 3x-19) =8( x-4)\\
\\
3x-19=2( x-4)\\
\\
3x-19=2x-8\\
\\
3x-2x=19-8\\
\\
x=11\ cm
\end{array}$

The value of $x$ is $11 cm$.

Updated on: 10-Oct-2022

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