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:

12 cm

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