In $ \triangle \mathrm{XYZ} $, the bisector of $ \angle X $ intersects $ Y Z $ at $ M $. If $ X Y=8, X Z=6 $ and $ M Z=4.8 $, find YZ.

Given:

In \( \triangle \mathrm{XYZ} \), the bisector of \( \angle X \) intersects \( Y Z \) at \( M \).

\( X Y=8, X Z=6 \) and \( M Z=4.8 \).

To do:

We have to find \( YZ \).

Solution:

We know that,

An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Therefore,

$\frac{XY}{XZ}=\frac{YM}{MZ}$

$\frac{8}{6}=\frac{YM}{4.8}$

$YM=\frac{4.8\times4}{3}$

$YM=6.4$

$\Rightarrow YZ=YM+MZ=6.4+4.8=11.2\ cm$

Hence, the value of $YZ$ is $11.2\ cm$.