Question

Given a rectangular area, how do I find the largest possible perimeter?

Answer 1

Trick question; the answer is undefined.

For rectangles, we have:
`A=lw`
`P=2(l+w)`

We can rearrange:
`l=A/w`
Because of symmetry, we want to look for the largest `l`. However, we can make `l` as big as we want by making `w` as small as needed. Therefore `l` goes to infinity which makes `P` go to infinity, so the answer is undefined.

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.