In a right- angle triangle ABC, AB = 15cm, BC = 20cm and AC = 25cm. further, BP is the perpendicular on AC. What is the difference in the area of triangles PAB and PCB?

Correct option is B

Given:

AB = 15 cm, BC 20 cm and AC = 25 cm

BP is perpendicular on AC.

Solution:

Since, 15, 20, and 25 Pythagorean triplet the triangle is a right-angle triangle.

We know that,

AP = AB²/AC

=> AP = 15²/25 = 9cm

PC = BC²/AC

=> PC = 20²/25 = 16cm

BP = (AB × BC)/AC

=> BP = (15 × 20)/25 = 12cm

Area of ΔAPB = (AP × BP)/2

=> 9 × 12/2 = 54cm²

Area of ΔBPC = (BP × PC)/2

=> 12 × 16/2 = 96cm²

Difference between the area of both triangles,

=> 96 - 54 = 42cm²

∴ The correct answer is 42cm².