Solution
First of all the maximum area is always a square. You can get the answer first to check your work later.
1000/4=250 feet
One side is not needed so add that length to the non-parallel side.
250 + 250=500 feet is the length and 250 feet is the width(s)
A=500*250
A=125000 square feet
Doing the algebra...
P = L +2w
1000 = L+ 2w
100 - 2w = l
Area = Length x Weight
A=(1000-2w)w
A=1000w-2w²