The hypotenuse is 13 m. One of the shorter sides is 7 m longer than the other. Find the length of the shortest side.

Question

Although I could figure this out using the Pythagorean Triples (13, 12, 5), I would like to know how to figure this out without using the triple. Thank you for the help.

Answer 1

Let x = length of the shortest leg

Then x+7 = length of the longer leg

Using the Pythagorean Theorem, x² + (x+7)² = 13²

x² + x² + 14x + 49 = 169

2x² + 14x - 120 = 0

x² + 7x - 60 = 0

(x - 5)(x + 12) = 0

x = 5 or -12

Since x can't be negative, we know that x = 5

Lengths of sides: 5, 12, 13