If all you are given is the perimeter then you can have several areas, one of which will be the maximum area and one of which will be the minimum area.
I am assuming that the length and width both have to be integers.
If not, then the number of possibilities will be endless.
For Example:
2L + 2W = P
L = length
W = width
P = perimeter = 36
formula becomes:
2L + 2W = 36
solve for L to get:
L = 18 - W
start from a width of 1 and work your way up to get the area and the perimeter each time based on the formula that L = 18 - W
you will get:
W L P A
1 17 36 17
2 16 36 32
3 15 36 45
4 14 36 56
5 13 36 65
6 12 36 72
7 11 36 77
8 10 36 80
9 9 36 81 ***** maximum area when L = W
10 8 36 80
etc...
they repeat from here on, i.e. 8*10 = 10*8, 7*11 = 11*7, etc.
Your maximum area is when L and W are closest in value to each other.
Your minimum area is when L and W are furthest apart in value from each other.