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Question

A 25foot ladder leans against a building. As the bottom of he ladder at point A slides away from the building, the top of the ladder, B, slides from a height of 24 feet above the ground to a height of 16 feet. How many feet did the bottom of the ladder slide?

A
7
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B
8
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C
9
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D
12.2
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E
19.2
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Solution

The correct option is C 12.2
In ABC
AB2=BC2AC2
AB2=(25)2(24)2
AB2=625576
AB2=49
AB=49
AB=7
When ladder slides from the height of 24 feet to height of 16 feet then the new position of the ladder on the bottom is point E
ADE
AE2=DE2AD2
AE2=(25)2(16)2
AE2=625256
AE2=369
AE=369
AE=19.2

the bottom of the ladder slide = AEAB=19.27=12.2

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