Question 256030
We need two formulas:
(i) {{{P = 2L + 2W}}}
(ii) {{{A = LW}}}
We are told that the perimeter is 230, so (i) becomes 
(iii) {{{230 = 2L + 2W}}}
or
(iv) {{{115 = L + W}}}
step 1 - solve (iv) for L and we get
(v) {{{L = 115 - W}}}
step 2 - substitute (v) into (ii) to get
(vi) {{{A = (115-W)(W)}}}
writing (vi) in vertex form, we get
(vii) {{{-1(W-57.5)^2 + 57.5^2}}}
So, when W = 57.5, L = 57.5 and the max area is 3306.25 ft sq.