Question

the perimeter of a right angled triangle is 60 centimetres it hypotenuse is 26 cm find the area?

Answer 1

let a,b,c are the height , base and hypotenuse.
area of the triangle will be (1/2)ab
a +b+c=60cm (given)
a+b+26=60cm
a+b=34cm (consider it as equation 1)

by Pythagoras theorem
a²+b²=c²=26²(consider it as equation 2)

a+b=34cm ( using equation 1)
squaring both the side
(a+b)²=34²=1156
a²+b²+2ab=1156 ( using identity (a+b)²)
2ab= 1156-(a²+b²)
2ab=1156-26²(using equation 2)
2ab= 1156-676=480
multiplying 1/4 on both sides
(1/4)×2ab=(1/4)×480

(1/2)ab=120cm²
hope it helped