Question

The perimeter of a right triangle is 24 cm. If its hypotenuse is 10 cm, find its area.

Answer 1

Let the side be a, b, c and let c be the hypotenuse and a, b will be base or height

then a+b+c = 24

a+b+10 = 24

a+b = 24-10 = 14 ----------------- 1

a2+b2 = 102  ----------------  2

From  1 we get a = 14-b

put the value of a in equation 2

(14-b)2+b2 = 100

196-28b+b 2+b 2 =100

2b2-28b+196-100 = 0

b2-14b+48 = 0

(b-6)(b-8) = 0  so b =6 or 8 then we will get a= 8 or 6 using equation 1

so the area of triangle is 1/2 bxh = 1/2 x 8x 6 = 24 cm2