[FredZarguna]

Tell the idiot teacher that the system being solved is:

LW = 12
2L + 2W = P

This is a system of 2 equations in 3 unknowns. It therefore has an infinite number of solutions. The minimum solution is for a square:

L² = 12
4L = P

This is solvable, the answer is L = 2√3. which gives a perimeter of 4L = 8√3

The maximum perimeter is infinity. By lengthening the length and shortening the width, you can obtain any perimeter between 8√3 (≈ 13.86) and ∞.

[Perdogg]

since your material has to be measure in L-squared your answer is incorrect.