Question

The shorter leg of a right triangle is two less than the hypotenuse. The longer leg is one less than the hypotenuse. Find all three sides of the triangle. HELP TEST!

Answer 1

x = 5

Explanation:

using the Pythagorean theorem:

(x-1)² + (x-2)² = x²

x²-2x+1 + x²-4x+4 = x²

reduce:

2x²-6x+5 = x²

subtract x² from each side:

x²-6x+5 = 0

(x-1)(x-5) = 0

x=1 but because shorter leg would be 0, a triangle would be impossible.

x=5