Consider a convex quadrilateral whose diagonals have lengths p,q and whose area is A.
What is the maximum area of a rectangle that circumscribes the given quadrilateral?
Question to Ahmed about the definition of "circumscribe": Are we talking about rectangles that completely contain the quadrilateral? Or is it sufficient that the corners of the quadrilateral are *somewhere* on the 4 lines that define the rectangle? I am not sure the notion of "circumscribe" is so well-defined in the general case...
If this is about the former situation, some cases will have "boundary solutions" for the given maximization problem, therefore I doubt very much there is a nice formula for it.
In the latter situation, the formula must be some function of p, q and the angle of the diagonals, or - thanks to Larry's observation - of p, q and A, as the problem statement suggests.
Posted by JLo
on 2020-01-07 16:16:50