Calculus
posted by Anonymous .
A fence 2 feet tall runs parallel to a tall building at a distance of 6 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?

Let the ladder length be d
Let the base of the ladder be x feet from the fence, and hit the wall at height h.
from similar triangles,
2/x = h/(6+x)
h = 2(x+6)/x
d^2 = (6+x)^2 + h^2
= (x+6)^2 + 4(x+6)^2/x^2
= (x+6)^2 * (1 + 4/x^2)
d^2 (and therefore d) has a minimum at x = 2.9
d^2 = 116.88
d = 10.8 ft