# Mathematics

A Ladder AB, of length 13m, rests against a vertical wall with its foot on a horizontal floor at a distance of 5meters from the wall. When the top of the ladder slips down a distance x meters on the wall, the foot of the ladder moves out x meters. Find x.

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1. It is like triangle.
a^2+b^2=c^2
you know that one of the side and hyp. so, you can find the ohter by pluging in like this:
5^2+b^2= 13^2
25+b^2=169
b^2=144
b= 12

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2. Actually, it is calculus of differentials.

C^2=a^2 + b^2
Take the differential
2C dC=2a da + 2b db
but dC is zero (C is held constant), so

da=- (b/a)db
so whatever one side slips down the wall, so the other side slips along the floor in the ratio cited.

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bobpursley

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