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...

Let x be the
distance from where the ladder hits the ground to the fence, and let h be the height on the wall
where the ladder hits the wall, and let l be the length of the ladder.

Then
using the pythagorean theorem we get :

Also, the triangles formed by the wall and the fence are similar, so:

so

Then