The longer leg of a right triangle is 8 more than the shorter leg. The hypotenuse is 6 more than the longer leg. Find all three sides.
Let the longer leg = x
The shorter leg = x - 8
The hypotenuse = x + 6
By Pythagoras
(x - 8)^2 + x^2 = ( x + 6)^2 simplify
x^2 - 16x + 64 + x^2 = x^2 + 12x + 36
2x^2 - 16x + 64 = x^2 + 12x + 36
x^2 - 28x + 28 = 0
Using the Quad Formla
x = ( 28 ± sqrt [ 28^2 - 4*28] ) / 2
x ≈ 1.04 reject
x ≈ 27 = the longer leg
x - 8 ≈ 19 = the shorter leg
x + 6 ≈ 33 the hypotenuse