Question

The hypotenuse of a right triangle is one inch longer than the longer leg. The shorter leg is seven inches shorter than the longer leg. Find the length of the hypotenuse.

Answer 1

Length of hypotenuse is 13 unit or 5 unit

Explanation:

Find;

Length of hypotenuse

Computation;

Assume;

Length of hypotenuse = h

Length of longer leg = h - 1

Length of shorter leg = h - 1 - 7

Using Pythagorean theorem

hypotenuse² = longer leg² + shorter leg²

h² = (h - 1)² + (h - 1 - 7)²

h² = (h - 1)² + (h - 8)²

h² = h² - 2h + 1 + h² - 16h + 64

h² = 2h² - 18h + 65

h² - 18h + 65 = 0

h² - 13h - 5h + 65 = 0

h(h - 13) -5(h - 13)

(h - 13)(h - 5)

So,

Length of hypotenuse is 13 unit or 5 unit