Question

The difference of the length of perpendicular sides of right triangle is 10cm. Its area is 72 square cm. Find the length of the perpendicular side

Answer 1

Answer:

8 cm and 18 cm

Step-by-step explanation:

Let the smaller perpendicular be x.

Larger perpendicular = x+10

Area = 1/2 × Base × Height

Given area = 72 cm²

=> 72 = 1/2 × x × (x+10)

=> 144 = x²+10x

=> x²+10x-144 = 0

=> x²-8x+18x-144 = 0

=> x(x-8)+18(x-8) = 0

=> (x+18)(x-8) = 0

=> x = -18 or x = 8

Neglecting negative value of x,

Smaller perpendicular = 8 cm

Larger perpendicular = (8+10) cm = 18 cm