The shorter leg of a right triangle is 7 less than the longer leg. If the hypotenuse is 1 more than the longer leg, find the length of the hypotenuse.

Answer 1

Let x = length of the longer leg

Then, x - 7 = length of shorter leg and x + 1 = length of the hypotenuse

So, by the Pythagorean Theorem, x² + (x - 7)² = (x + 1)²

x² + x² - 14x + 49 = x² + 2x + 1

x² - 16x + 48 = 0

(x - 12)(x - 4) = 0

So, x = 12 or x = 4

If x = 4, then x - 7 < 0, so x = 12

Length of hypotenuse = x + 1 = 13