What are the lengths of its sides? (Enter your answers from smallest to largest.)

Question

A right triangle has legs of lengths x and 2x − 1 and a hypotenuse of length

2x + 1. What are the lengths of its sides? (Enter your answers from smallest to largest.)

Answer 1

Per the Pythagorean Theorem:

(x)^2 + (2x - 1)^2 = (2x + 1)^2

x^2 + 4x^2 - 4x + 1 = 4x^2 + 4x + 1

x^2 - 4x + 1 = 4x + 1

x^2 - 8x = 0

x(x-8) = 0

x = 8

2x - 1 = 15

2x + 1 = 17