Question
The perimeter of a right triangle is 24 cm. If its hypotenuse is 10 cm, find its area.
Solution
Let the sides forming the right angle be a cm and b cm. Then,
a + b + 10 = 24
⇒ a + b = 14 ...(1)
Also, a2 + b2 = (10)2
⇒ a2 + b2 = 100 ...(2)
We know that
(a + b)2 = a2 + b2 + 2ab
⇒ (14)2 = 100 + lab
⇒ 2ab = 96
⇒ ab = 48 ...(3)
Also, (a – b)2 = a2 + b2 – 2ab
= 100 – 2 x 48 = 100 – 9b
= 4 | if a > b
⇒ a – b = 2 ....(4)
Solving (1) and (4), we get a = 8 cm b = 6 cm
