SOLUTION: A 25-foot ladder reaches 24 feet up the side of building. Then the top of the ladder slides down 4 feet. How many additional feet does the bottom of the ladder slide out from the b

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Question 262989: A 25-foot ladder reaches 24 feet up the side of building. Then the top of the ladder slides down 4 feet. How many additional feet does the bottom of the ladder slide out from the base of the building?

Answer by mananth(16946) About Me  (Show Source):
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A 25-foot ladder reaches 24 feet up the side of building. Then the top of the ladder slides down 4 feet. How many additional feet does the bottom of the ladder slide out from the base of the building?

25^2= 24^+x^2 x distance from the wall
625-576=49
Sqrt49=7
The ladder is 7 ft from the wall in the first position

Second position
Let it slide x feet.
Vertical slide is 4 ft : so vertical height = 20
25^2= 20^2 + (x+7)^2
625= 400 + x^2 +14x+49
X^2 +14x – 176=0
X^2 +22x-8x+176=0
X(x+22)-8(x+22)=0
(x+22)(x-8)=0
So x= 8
It slides by 8 feet.