Question:
In a triangle \(PQR\), \(PS\) is the angle bisector of \(\angle P\). \(PQ=3\), \(QS=2\) and \(SR=3\), then \(PR=\)
In a triangle \(PQR\), \(PS\) is the angle bisector of \(\angle P\). \(PQ=3\), \(QS=2\) and \(SR=3\), then \(PR=\)
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If an angle bisector divides the opposite side, use the ratio of adjacent sides.
Updated On: Jul 15, 2026
- \(3\)
- \(4\)
- \(3.5\)
- \(4.5\)
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The Correct Option is D
Solution and Explanation
By Angle Bisector Theorem:
\[
\frac{PQ}{PR}=\frac{QS}{SR}
\]
Substitute values:
\[
\frac{3}{PR}=\frac{2}{3}
\]
Cross multiply:
\[
9=2PR
\Rightarrow PR=\frac92=4.5
\]
Thus,
\[
\boxed{4.5}
\]
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