Question

The hypotenuse of isosceles right triangle is 10 cm find its area by heron's formula and pythagoras property

Answer 1

Step-by-step explanation:

Given a right angled isosceles triangle with a hypotenuse of 10 what is it’s area?

From Pythagoras: h*h = a*a+b*b

As the triangle is isosceles, the non-hypotenuse sides have the same length.

So: h*h = 2*a*a

=> a = root(h*h/2)

The area of the triangle is base * height / 2

So: area = a*a/2

=> root(h*h/2)*root(h*h/2)/2

=> h*h/4

=> 10 * 10 / 4

=> 25 square cm