By the Pythagorean theorem 50^2 = x^2 +(x +34)^2 2500 = 2x^2 +68x + 1156 x^2 +34x -672 = 0 (x -14)(x +48) = 0 x = 14 or -48
The distance from the wall to the base of the ladder is 14 ft.
_____ 7-24-25 is a Pythagorean triple. The dimensions here are double those values. It can be handy to know a few of the Pythagorean triples, as that can let you write down the answers to problems without having to go through the equations.
