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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Updated on: 10-Oct-2022

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