SOLUTION: A ladder of length 2x+1feet is positioned against a wall such that the bottom is x−1feet away from a wall. The distance between the floor and the top of the ladder is 2xfeet.

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Question 955844: A ladder of length 2x+1feet is positioned against a wall such that the bottom is x−1feet away from a wall. The distance between the floor and the top of the ladder is 2xfeet.
Find the length, in feet, of the ladder.
Assume that a right angle is formed by the wall and the floor.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2%2Bb%5E2=c%5E2
%28x-1%29%5E2%2B%282x%29%5E2=%282x%2B1%29%5E2
x%5E2-2x%2B1%2B4x%5E2=4x%5E2%2B4x%2B1 Subtract 4x%5E2%2B1 from each side.
x%5E2-2x=4x Subtract 4x from each side.
x%5E2-6x=0
x(x-6)=0
x=6ft
2x+1=2(6ft)+1=13 feet ANSWER: The ladder is 13 feet long.
CHECK:
%28x-1%29%5E2%2B%282x%29%5E2=%282x%2B1%29%5E2
%286-1%29%5E2%2B%282%286%29%29%5E2=%282%286%29%2B1%29%5E2
5%5E2%2B12%5E2=13%5E2
25%2B144=169
169=169