In $\vartriangle PQR$, if $PQ=6\ cm,\ PR=8\ cm,\ QS = 3\ cm$, and $PS$ is the bisector of $\angle QPR$, what is the length of $SR$?

Given: $PQ=6 cm,\ PR=8 cm,\ PS$ is the bisector of  such that: $QS=3\ cm$.

To do: To find the length of $SR$.

Solution:

As known the angle bisector of an angle in a triangle divides the opposite side into two segments which are in proportion to the other two sides.

$\Rightarrow \frac{QS}{SR}=\frac{PQ}{PR}$

$\Rightarrow \frac{3}{SR}=\frac{6}{8}$

$\Rightarrow SR=\frac{8\times3}{6}$

$\Rightarrow SR=4\ cm$

The angle bisector of an angle in a triangle divides the opposite side into two segments which are in proportion to the other two sides.

Hence, the length of $SR=4\ cm$.

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Updated on: 10-Oct-2022

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