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Question 283044: A 26 ft 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 rests against the wall is x + 14. Find the distance, x, from the base of the wall tithe bottom of the ladder. Please show steps in solving this word problem.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! A 26 ft 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 rests against the wall is x + 14. Find the distance, x, from the base of the wall tithe bottom of the ladder. Please show steps in solving this word problem.
You can imagine that the the ladder , the wall and the floor make a right angle.
The ladder is the hyotenuse
AND the floor and the wall form the legs of the right angled triangle.
26^2= x^2 + ( x+14)^2
676= x^2 +x^2 +28x +196
2x^2+28x-480 =0
2x^2 +40x -12x -480=0
2x(x+40)-12(x+40)=0
(2x-12)(x+40)=0
2x=12
x=6 feet distance from the base to the bottob of the ladder
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