two straight wires are attached at a point 24 feet above the base of a vertical pole standing on level ground. One wire is 5 feet longer than the other reaches a point on the ground 11 feet farther from the base. Find the length of each.

L^2 = x^2 + 24^2

(L+5)^2 = (x+11)^2 + 24^2

L^2 + 10L + 25 = x^2 + 22x + 11^2 + 24^2

From this subtract 1st equation

10L + 25 = 22x + 121

22x = 10L - 96

11x = 5L - 48

x = (5L - 48)/11

L^2 = ((5L - 48)/11)^2 + 24^2

121 L^2 = (5L - 48)^2 + 121*24^2

121 L^2 = 25L^2 - 480L + 4*24^2 + 121*24^2

96 L^2 + 480L - 125*24^2 = 0

L^2 + 5 L - 750 = 0

25 + 3000 = 3025 = 55^2

L = (-5 ± 55)/2 = -30, 25

L = 25

L + 5 = 30