Calculus
posted by Pete on .
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?

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/h7/h^2 dh x/h^2 dh
dx/dh (1/61/h)=1/h^2 (7x)
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.