If S is a point on side QR ofa triangle PQR such that QS = 10 cm. QR = 18 cm and ∠PSR = ∠QPR , then the length of PR will be:
Answer & explanation
Correct answer: option 2
We have,
QS = 10 cm
QR = 18 cm
∠PSR = ∠QPR
According to the question,
In ΔPQR and ΔSPR
∠PSR = ∠QPR
∠R = ∠R [common]
So, ΔPQR ~ ΔSPR
= \(\frac{ QR}{ PR }\) = \(\frac{ PR}{ SR }\)
= \(\frac{ 18}{ PR }\) = \(\frac{ PR}{8 }\)
= PR2 = 144
= PR = 12 cm