AB = 52 P_triangleABC - ?

The image shows a right-angled triangle ABC, with a circle inscribed in it. The radius of the inscribed circle is given as 8. The hypotenuse AB is given as 52. The triangle is right-angled at C. Let r be the inradius. The formula for the perimeter of a right-angled triangle in terms of its sides a, b and hypotenuse c is P = a + b + c. Also, for a right-angled triangle, the inradius r = (a + b - c) / 2. We are given r = 8 and c = 52. So, 8 = (a + b - 52) / 2. This implies a + b - 52 = 16, so a + b = 68. The perimeter P = a + b + c = 68 + 52 = 120.