Question

In need of some help please.

Answer 1

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.

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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.