SOLUTION: 25 + (x-1)^2 = C^2 this is the formula i came up with from the word question: A ladder is leaning against a building so that the distance from the ground to the top of the la

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Question 181933: 25 + (x-1)^2 = C^2
this is the formula i came up with from the word question:
A ladder is leaning against a building so that the distance from the ground to the top of the ladder in one foot less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 5 feet.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length of ladder


Since "the distance from the ground to the top of the ladder in one foot less than the length of the ladder.", this means that one leg of the triangle is x-1 ft. Also, we're given the other leg of 5 ft.


So this tells us that a=5, b=x-1 and c=x


a%5E2%2Bb%5E2=c%5E2 Start with Pythagorean's Theorem


5%5E2%2B%28x-1%29%5E2=x%5E2 Plug in a=5, b=x-1 and c=x


25%2B%28x-1%29%5E2=x%5E2 Square 5 to get 25


25%2Bx%5E2-2x%2B1=x%5E2 FOIL


25%2Bx%5E2-2x%2B1-x%5E2=0 Subtract x%5E2 from both sides.


-2x%2B26=0 Combine like terms.


-2x=0-26 Subtract 26 from both sides.


-2x=-26 Combine like terms on the right side.


x=%28-26%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=13 Reduce.


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Answer:

So the answer is x=13


So this means that the length of the ladder is 13 ft while the height that the ladder reaches on the building is 12 ft.