Posted by **Anonymous** on Friday, October 28, 2011 at 1:19pm.

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?

- Calculus -
**Steve**, Friday, October 28, 2011 at 4:49pm
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

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