Posted by **Pete** on Tuesday, July 13, 2010 at 2:47pm.

A fence 6 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

- Calculus -
**bobpursley**, Tuesday, July 13, 2010 at 3:10pm
Have you considered drawing a sketch?

let x be the distance from the fence to the ladder base, so x+7 is the distance to the building from the ladder base.

x/6=(x+7)/h where height at the building intercept.

dx/6=dx/h-7/h^2 dh -x/h^2 dh

dx/dh (1/6-1/h)=-1/h^2 (7-x)

but dx/dh=0 so

x must 7

so length can be figured from

length=2(sqrt (16+49))

check that, I did it quickly.

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