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 ?
Answer & explanation
Correct answer: option 1
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