What is length of shortest ladder?

Question

A fence 6 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?

Answer 1

A diagram is difficult to construct on this site. But, the shortest ladder is when the horizontal side is equal to the vertical side of the triangle that the ladder makes with the barn and ground.

This means that each is 12 ft.

So, the shortest ladder L is L² = (36/6 + 6)² + (6 + 6)2 or L² = 288 or L = 16.97 ft