I have ten meters of mesh fence. I want to make two enclosures for my rabbits who can’t stand each other (they can share a wall). What is the shape and the area of the largest enclosure (in terms of area) I can build? Each rabbit needs to have access to the same area. The shape can be arbitrary (although it would be nice if it were continuous or smooth to some extent, and each area contiguous).
Examples:
A square of 2x2m, divided by a 2m wall. Area: 4 square meters
A circle of radius 1.21m, divided by a wall. Area: ~4.58 square meters.
Is it possible to do better?
Does the entire boundary have to be made of the mesh? Especially relevant if this is for practical use rather than just a challenge since you could use e.g. two existing corners in a rectangular yard: cut the mesh in half, and use 5m to close off each corner. Making isosceles triangles out of each corner with the two equal length sides having length sqrt(25/2) ~= 3.535m gives areas of 6.25 sq. meters for each rabbit.
You could do even better if you happened to already have 3 walls of the appropriate lengths to partition off an area in as well… e.g. 2.5m x 5m = 12.5 sq m. for each rabbit if you have a rectangular yard surrounded by an existing wall where the back wall is 5m long and the other two sides are at least 2.5m long. That configuration is less likely for someone to already actually have though.
In my case, yes, because I don’t have much to attach the mesh wire to.