Question

Prove that if the hypotenuse of a right triangle is h and the radius of its incircle is r, then its area is r(h+r).

Answer 1

Let the perpendicular sides of right-angled triangle be a, d and hypotenuse be h then

Area of triangle = \(\frac{1}{2}\) ab

Radius of incircle of right angled triangle = 

∴ r = \(\frac{a+b-h}{2}\)