In ΔPQR, ∠Q = 90˚, PQ = 8 cm and PR = 17 cm. If the bisector of ∠P meets QR at S, then what is the length (in cm) of SR?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 10.2.
PR2 = PQ2 + QR2
⇒ 172 = 82 + QR2
⇒ QR2 = 225
⇒ QR = 15 cm
The angle bisector divides the opposite side in the ratio of the adjacent sides.
QS/SR = PQ/PR = 8/17
Let, QS = 8k, SR = 17k
Then, QR = QS + SR = 8k + 17k = 25k = 15 cm
⇒ k = 15/25 = 3/5
SR = 17k = 17 × (3/5) = 10.2 cm