Question

the hypotenuse of a right triangle is 70 inches long. one leg is 3 inch(es) longer than the other. find the lengths of the legs of the triangle. round your answers to the nearest tenth of an inch.

Answer 1

47.975, 50.975

Explanation:

hypotenuse = 70

x = 1st leg

x + 3 = 2nd leg

70² = x² + (x + 3)² = x² + x² + 6x + 9 = 2x² + 6x + 9

2x² + 6x + 9 = 4900

2x² + 6x² - 4891 = 0

use quadratic equation to solve for x:

a=2, b=6, c=-4891

x = 47.975, -50.975

Throw out the negative solution

Therefore, the 2 legs are:

47.975 and 47.975 + 3 = 50.975

Test the answers for correctness: 47.975² + 50.975² = 4900

√4900 = 70 = the hypotenuse