Angle-bisector area split inside a triangle:\nTriangle PQR has area 180 cm^2. Point S lies on QR, and PS is the angle bisector of ∠QPR. If PQ : PR = 2 : 3, find the area (in cm^2) of triangle PSR.

Introduction / Context:
The internal angle bisector divides the opposite side in the ratio of the adjacent sides. Hence, the areas of the two sub-triangles formed on that base are in the same ratio as the base segments.

Given Data / Assumptions:

• Total area(ΔPQR) = 180 cm^2.
• PQ : PR = 2 : 3 and PS is the internal angle bisector of ∠QPR.

Concept / Approach:
By the Angle Bisector Theorem, QS : SR = PQ : PR = 2 : 3. Because P is common vertex and the altitude from P to QR is common for ΔPQS and ΔPSR, areas are proportional to their bases on QR.

Step-by-Step Solution:

Verification / Alternative check:
A quick check: the other sub-area is 72; 72 + 108 = 180 matches the total area.

Why Other Options Are Wrong:
90, 144, 72, 120 do not equal 3/5 of 180.

Common Pitfalls:
Confusing the 2:3 as area(ΔPQS):area(ΔPSR) = 2:3 but then assigning the wrong sub-triangle to the larger part; ensure PSR corresponds to the segment SR (ratio 3).

Final Answer:
108