Help me slove this problem

Question

Find the length of the shorter leg of a right triangle if the longer leg is 4 feet more than the shorter leg and the hypotenuse is 4 feet less than twice the shorter leg

Answer 1

Let x = measure of shorter leg

Then x+4 = measure of longer leg

And 2x-4 = measure of hypotenuse

By Pythagorean Theorem the sum of the squares of the legs equals the square of the hypotenuse:

x² + (x+4)²= (2x-4)²

x²+x²+8x+16= 4x²-16x+16

0=2x²-24x

2x(x-12)=0

x=0 or x = 12 (rule out the x = 0)

Check:

Sides are 12, 16 , 20 (this set is a multiple of the Pythagorean triple 3,4,5; so clearly a right triangle)

But:

12²+16²=? 20²

144 + 256 =? 400 (check)