The diagonals of a convex quadrilateral are mutually perpendicular.
The sum of the lengths of the diagonals is 10. We want to find the
maximum possible area of such a quadrilateral.
Let us denote by and the lengths of the two diagonals.
Then the area of the quadrilateral is the following function of
and :
If we solve for in terms of , we can reexpress this
area as the following function of alone:
Thus we find that the maximum area is