Given two crossed ladders resting against two parallel walls.

The feet of the ladders are each at the base of the opposite wall.

Denote the height at which they cross by h and the lengths of the ladders by m and n.

1. Find the heights (h1,h2) at which the ladders touch the walls.

2. Show that 2*h is the harmonic average of h1 and h2.

3. Evaluate the distance (D) between the walls.

4. Provide an example such that m,n,h,h1,h2
and D are integers.