Any and all help is appreciated. I've been working this problem all day and at this point I keep going around in circles...

Consider two buildings with heights h1 and h2, and an alleyway between them of length L. Suppose that two supports are attached in the manner shown below.

Yfrog Image : yfrog.com/0strigproblemp

We call the height at which the supports cross, X. We divide L into two parts: M and L-M. Using similar triangles with h1, h2, X, M, and L-M, show that the height of the crossing, X, is given by the equation: x = (h1*h2)/(h1+h2)