This can be done really simply. Area of the triangle is equal to s*r.
A = s*r , r is the radius and s = (a+b+c)/2 is called semiperimeter or half of the triangles perimeter. In your case you can easily find the Area, a*b/2 and using the pythagorean theorem find the third side. And then just compare the ttwo equations a*b/2 = (a+b+c)*r/2. Hope this helps