The longer leg of a right triangle is 1 meter longer than the shorter leg. The hypotenuse is 1 meter shorter than twice the shorter leg. Find the length of the shorter leg of the triangle.

Question

The longer leg of a right triangle is 1 meter longer than the shorter leg. The hypotenuse is 1 meter shorter

than twice the shorter leg. Find the length of the shorter leg of the triangle.

Answer 1

x = length of shorter leg

x+1 = length of longer leg

2x - 1 = length of hypotenuse.

Per Pythagorean Theorem:

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

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

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

0 = 2x^2 - 6x

0 = 2x (x - 3)

x = 3

longer leg = 4

hypotenuse = 5

3-4-5 right triangle

Answer 2

(2s - 1)² = (s + 1)² + s²

Can you solve for s and answer?