Question

If the hypotenuse of a right-angled triangle is h and it's inradius is r, then find it's area.

Answer 1

Let PB = BQ = r

AP = AR = b - r

CQ = CR = a - r

AR + CR = h

a + b - 2r = h

a + b = h + 2r

Area = A = rS

$\Rightarrow$ A = r$\frac{a+b+h}{2}$

$\Rightarrow$ A = r$\frac{h+2r+h}{2}$

$\Rightarrow$ A = r(h + r)