How Do You Bisect an L-Shaped Figure into Equal Areas?

[Hurkyl]

I wonder if it would not be easier to simply write down equations defining the bisector in terms of the various parameters, and see if it's solvable with square roots.

 

[NateTG]

I wonder if it would not be easier to simply write down equations defining the bisector in terms of the various parameters, and see if it's solvable with square roots.

Probably, but I hadn't thought of doing that.