A fence 3 feet tall runs parallel to a tall building at a distance of 3 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?

Answer 1

Draw a diagram. If the ladder's length is z, and the base of the ladder is x feet from the fence, then by similar triangles, you can see that

z/(x+3) = √(x^2+9)/x
z = (x+3)√(x^2+9)/x
dz/dx = (x^3-27) / (x^2 √(x^2+9))
dz/dx=0 when x=3

z(3) = 6√18/3 = 6√2