In $ \Delta \mathrm{XYZ}, \mathrm{S} $ and $ \mathrm{T} $ are points of $ \mathrm{XY} $ and $ \mathrm{XZ} $ respectively and ST $ \| \mathrm{YZ} $. If $ \mathrm{XS}=4 \mathrm{~cm} $, $ \mathrm{XT}=8 \mathrm{~cm}, \mathrm{SY}=x-4 \mathrm{~cm} $ and $ \mathrm{TZ}=3 x-19 \mathrm{~cm} $ find the value of $ x $.
Given:
In \( \Delta \mathrm{XYZ}, \mathrm{S} \) and \( \mathrm{T} \) are points of \( \mathrm{XY} \) and \( \mathrm{XZ} \) respectively and ST \( \| \mathrm{YZ} \).
\( \mathrm{XS}=4 \mathrm{~cm} \), \( \mathrm{XT}=8 \mathrm{~cm}, \mathrm{SY}=x-4 \mathrm{~cm} \) and \( \mathrm{TZ}=3 x-19 \mathrm{~cm} \).
To do:
We have to find the value of \( x \).
Solution:
We know that,
The line drawn parallel to one side of a triangle and cutting the other two sides divides the other two sides in equal proportion.
Therefore,
$\frac{XS}{SY}=\frac{XT}{TZ}$
$\frac{4}{x-4}=\frac{8}{3x-19}$
$4(3x-19)=8(x-4)$
$12x-76=8x-32$
$12x-8x=76-32$
$4x=44$
$x=\frac{44}{4}$
$x=11\ cm$
Hence, the value of $x$ is $11\ cm$.
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