Question

Prove that when x > 1, a triangle with side lengths a = x2 − 1, b = 2x, and c = x2 + 1 is a right triangle. Use the Pythagorean theorem and the given side lengths to create an equation. Use the equation to show that this triangle follows the rule describing right triangles. Explain your steps.

Answer 1

First we need to see the pythagorean formula which is

$a^2 + b^2 = c^2$

Substituting the given values of a,b , we will get

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

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

$= x^4 +1 +2x^2$

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

And

$(x^2 +1)^2 = c^2$

So we have

$a^2 + b ^2 = c^2$

So the given triangle is a right triangle .