A fence  ft tall runs is parallel to a tall building at a distance of  ft from the building.

Use the ladder from the ground to reach the wall of the building over the fence.

Draw the figure using the above data.

Observe the figure.

Use the similar triangles properties,

From the pythagorean theorem,

Apply derivative on each side with respect to .

The length of the ladder is minimum when its first derivative becomes zero.

Equate  to zero.

Substitute  in .

Therefore the minimum length of the ladder is  ft.

The minimum length of the ladder is  ft.