Find the sides of a triangle

Question

The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. The length of the hypotenuse is 6ft more than twice the length of the shorter leg. Find the side lengths of the triangle.

Answer 1

Let x = the length of the shorter leg

Let 2x + 4 = the length of the longer leg

Let 2x + 6 = the length of the hypotenuse

x² + (2x+4)² = (2x+6)²

x² + 4x² +16x +16 = 4x² + 24x + 36
5x² + 16x + 16 = 4x² + 24x + 36

x² - 8x - 20 = 0

(x-10)(x+2) = 0

x-10=0     x+2=0

x=10 feet     x=-2, not a logical answer

2x+4 =2(10)+4 = 24 feet

2x+6 = 2(10)+6 = 26 feet