Hypotenuse question

Question

a right triangles hypotenuse is 10 inches long. The length of one leg of a right triangle is 2 inches more than the second leg. What are the lengths of the legs of the triangle

Answer 1

L₁=L₂+2

According to Pythagorean theorem h²= (L₁)² + (L₂)²=(L₂+2)²+(L₂)²

Now, solve the quadratic equation for L₂, and then find the second leg L₁=L₂+2

Answer 2

length of legs: x, x + 2

by Pythagorean Theorem:

x^2 + (x+2)^2 = 10^2

x^2 + x^2 + 4x + 4 = 100

2x^2 + 4x - 96 = 0

x^2 + 2x - 48 = 0

(x + 8)(x-6) = 0

x = 6 is only valid solution

x+2 = 8

legs are 6 and 8 inches