CDS 2024 · PYQ · Right Triangles / Geometry · medium
In a right-angled triangle ABC, AB = 15 cm, BC = 20 cm and AC = 25 cm. Further, BP is the perpendicular on AC. What is the difference in the area of triangles PAB and PCB?
A.40 square cm
B.42 square cm✓ Correct
C.45 square cm
D.48 square cm
Explanation
The triangle is right-angled at B (15²+20²=25²). BP = (15×20)/25 = 12 cm. AP = 15²/25 = 9 cm, PC = 20²/25 = 16 cm. Area of PAB = (1/2)(9)(12) = 54. Area of PCB = (1/2)(16)(12) = 96. Difference = 96 - 54 = 42 sq cm.
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