SOLUTION: help ): can you explain this step by step? A 50 ft ladder is leaning against the side of a building. The top of the ladder reaches 34 ft higher than the distance the base of the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: help ): can you explain this step by step? A 50 ft ladder is leaning against the side of a building. The top of the ladder reaches 34 ft higher than the distance the base of the      Log On


   

Question 761542: help ): can you explain this step by step?
A 50 ft ladder is leaning against the side of a building. The top of the ladder reaches 34 ft higher than the distance the base of the ladder is from the wall. Find the distance from the wall to the base of the ladder.
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Imagine the wall meets the floor at origin. Vertically upward on th y axis is 34+w where w is the same as the distance from the origin to the other end of the ladder. From the origin to the end of the ladder on the horizontal axis is this length w. The ladder itself forms the hypotenuse of this triangle form.

highlight%28w%5E2%2B%28w%2B35%29%5E2=50%5E2%29 and need to solve for w.

w%5E2%2Bw%5E2%2B70w%2B35%5E2=50%5E2
2w%5E2%2B70w%2B%2835%5E2-50%5E2%29=0 you see the difference of two squares?
2w%5E2%2B70w%2B%2835-50%29%2835%2B50%29=0
2w%5E2%2B70w%2B%28-15%29%2885%29=0
2w%5E2%2B70w-1275=0

w=%28-70%2Bsqrt%284900-4%2A2%2A%28-1275%29%29%29%2F%284%29
w=%28-70%2Bsqrt%284900%2B8%2A1275%29%29%2F4
%28-70%2Bsqrt%2815100%29%29%2F4
%28-70%2B10%2Asqrt%28151%29%29%2F4
%28-35%2B5%2Asqrt%28151%29%29%2F2
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About 13.2 feet.
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