PQR is a triangle, whose area is 180 cm². S is a point on side QR, such that PS is the angle bisector of ∠QPR. If PQ : PR = 2 : 3, then what is the area (in cm²) triangle PSR?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{PQ}}{{PR}} = \frac{2}{3} \cr & \therefore \frac{{{\text{ar }}\Delta PSR}}{{{\text{ar }}\Delta PQR}} = \frac{3}{{2 + 3}} = \frac{3}{5} \cr & 5{\text{ units}} = 180 \cr & 3{\text{ units}} = \frac{{180}}{5} \times 3 = 108 \cr & {\text{Area of }}\Delta PSR = 108{\text{ c}}{{\text{m}}^2} \cr} $$