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.

Question

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.

(I couldn't find this answer, can anyone please please help me. With the math equation too? Not the answer only please. So I know what to do it. Thx.)

^quen^ · Answer

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

bobpursley · Answer

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.