Rule #1 - Name Stuff
It's a rectangle.
L = Length > 0
W = Width > 0
Rule #2 - Dump Information from Your Brain
Perimeter(L,W) = 2*L + 2*W > 0
Area(L,W) = L*W > 0
If anything else ABOUT RECTANGLES comes to mind, write it down, too.
Rule #3 Search for clues.
"field of a given area" -- Aha! Here is a parameter that doesn't move around. This gives:
L = Area/W (Or W = Area/L if you like. I'll use the first.)
Perimeter(W) = 2*(Area/W) + 2*W
I suspect you can now minimize Perimeter(W) with respect to the single variable "W".
Finally, you must ask how W relates to L. This is the exciting part of the problem!