In Delta PQR,the bisector of angle P intersec | vedclass

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(D) According to the Angle Bisector Theorem,if a ray bisects an angle of a triangle,then it divides the opposite side into segments that are proportio

Vedclass · Accepted Answer

$7.5$

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(D) According to the Angle Bisector Theorem,if a ray bisects an angle of a triangle,then it divides the opposite side into segments that are proportional to the other two sides of the triangle.In $\Delta PQR$,since $PS$ is the bisector of $\angle P$,we have the ratio:$\frac{PQ}{PR} = \frac{QS}{SR}$Given values are $PQ = 5$,$QS = 2$,and $SR = 3$.Substituting these values into the formula:$\frac{5}{PR} = \frac{2}{3}$By cross-multiplying,we get:$2 	imes PR = 5 	imes 3$$2 	imes PR = 15$$PR = \frac{15}{2} = 7.5$Therefore,the length of $PR$ is $7.5$.

In $\Delta PQR$,the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $QS = 2$,$PQ = 5$ and $SR = 3$,find $PR$.

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