Question

The shorter leg of the right triangle is 8 less than the hypotenuse. The longer leg is 1 less than the hypotenuse. Find the perimeter of the triangle.

Answer 1

Hypotenuse = h
leg1 = h-8
leg2 = h-1

h² -(h-8)² = (h-1)²

h² - [h² -16h +64] = h² -2h +1
16h -64 = h² -2h +1
h² -18h + 65 = 0

hypotenuse = 13
leg1 = 13-8 = 5
leg2 = 13-1 =12

Perimeter = 13 + 5 + 12 = 30