In ΔPQR, S is a point on the side QR such that PS is the bisector of ∠QPR. If PQ 12 cm, QS = 3 cm and QR = 7 cm, then what is the length of side PR ?

18 cm

We know that,

According to the angular bisector property of the triangle, the angular bisector divides the opposite sides in a proportion equal to the remaining sides.

PQ = 12 cm

QS = 3 cm

QR = 7 cm

SR = QR - QS

So,  SR = 7 - 3 = 4 cm

In Δ PQR using angular bisector theorem, we get

\(\frac{PQ}{PR}\) = \(\frac{QS}{SR}\)

= \(\frac{12}{PR}\)= \(\frac{3}{4}\)

= PR = 16 cm