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

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(A) According to the Angle Bisector Theorem, the bisector of an angle of a triangle divides the opposite side into segments that are proportional to t

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(A) According to the Angle Bisector Theorem, the bisector of an angle of a triangle 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 $QR = 9.6$ and $QS = 4$, we can find $SR$ as: $SR = QR - QS = 9.6 - 4 = 5.6$.Substituting the known values into the theorem: $\frac{5}{PR} = \frac{4}{5.6}$.Cross-multiplying gives: $4 	imes PR = 5 	imes 5.6$.$4 	imes PR = 28$.$PR = \frac{28}{4} = 7$.Therefore, the length of $PR$ is $7$.

In $\Delta PQR$, the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ = 5$, $QS = 4$ and $QR = 9.6$, find $PR$.

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