SOLUTION: Initially, a 25-foot ladder rests against a vertical wall such that the top of the
ladder is 24 feet from the ground. Then, Nathan moves the base of the ladder
farther out from t
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Question 332729: Initially, a 25-foot ladder rests against a vertical wall such that the top of the
ladder is 24 feet from the ground. Then, Nathan moves the base of the ladder
farther out from the wall so that the top of the ladder slides down until resting
against the wall at a point 20 feet above the ground. Given the wall is
perpendicular to the ground, how far did Nathan move the base of the ladder?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Initially, a 25-foot ladder
24 feet from the ground.
Nathan moves the base of the ladder by x feet
.
INITIAL POSITION
d^2= 25^2-24^2
d^2=625-576=49
d=7 feet.
..
AFTER SHIFTING
Let the ladder be shifted to 20 feet height .
let the foot of the ladder move x feet
The distance from the wall will be x+7 feet
..
ladder = 25 feet
lowered height vertically = 20 feet
..
(x+7)^2+20^2=25^2
x^2+14x+49+400=625
x^2+14x-176=0
x^2+22x-8x-176=0
x(x+22)-8(x+22)=0
(x+22)(x-8)=0
x= 8 feet.
Nathan moved the ladder on ground by 8 feet.
the ladder will be 8+7 =15 feet from the ground after shifting
..
CHECK
15^2+20^2=225+400=625
sqrt 625 = 25 the length of the ladder
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