The longer leg of a right triangle is 8 more than the shorter leg. The hypotenuse is 10 more than the longer leg. Find all three sides.
+128448 Let the shorter leg = x
The longer leg x + 8
The hypotenuse x + 8 + 10 = x + 18
By rhe Pythagorean Theorem, we have
x^2 + ( x + 8)^2 = (x + 18)^2 simplify
x^2 + x^2 + 16x + 64 = x^2 + 36x + 324
2x^2 + 16x + 64 = x^2 + 36x + 324
x^2 - 20x - 260 = 0 complete the square on x
x^2 - 10x + 100 = 260 + 100
(x - 10)^2 = 360 take the positive roor
x - 10 = sqrt (360)
x - 10 = 6sqrt (10)
x = 6sqrt (10) + 10 = shorter leg
x + 8 = 6sqrt (10) + 18 = longer leg
x + 18 = 6sqrt (10) + 28 = hypotenuse
