Given a rectangular area, how do I find the largest possible perimeter?
Trick question; the answer is undefined.
For rectangles, we have:
We can rearrange:
Because of symmetry, we want to look for the largest
If the question is reversed, where we are looking for the largest area given a perimeter, then we would have a question that has a solution.
Or you can reverse the question to we are looking for smallest perimeter given a rectangular area; this too would have a solution.