A 10-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 2 ft longer that the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.
x and x + 2
x^2 +(x+2)^2 = 100
x^2 + x^2 + 4 x + 4 = 100
2 x^2 + 4 x = 96
x^2 +2 x - 48 = 0
(x-6)(x+8) = 0
x = 6
x+2 = 8