Question 300400: a 26ft. long ladder rests against a wall. The distance from the base of the wall to the bottom of the ladder is x. The height at which the ladder rest against the wall is x + 14. Find the distance, (x) from the base of the wall to the bottom of the ladder.
Answer by marolstr(3)   (Show Source):
You can put this solution on YOUR website! The Pythagorean theorem states that a^2 + b^2 = c^2 for right triangles, which this is. So, if x is a and x+14 is b (it doesn't matter which is which), you can assume that
x^2 + (x+14)^2 = 26^2, which, if you expand the (x+14)^2, gives
2x^2 + 28x + 196 = 676
Now you can move 676 over to the right side of the equation.
2x^2 + 28x -480 = 0
Dividing everything by 2 will make it easier to factor:
x^2 + 14x - 240 = 0
This factors into (x+24)(x-10)=0
The solutions of the equation are x = -24 and x = 10, but since this is a real length you're trying to find, it can't be negative.
So, x = 10. It is the distance from the base of the wall to the bottom of the ladder. If you need to find x + 14, you can substitute x = 10 to get 10+14=24.
Hope I helped!
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