Farmer Ed has 7000 meters of fencing and wants to enclose a rectangular plot that borders on a river. If farmer Ed does not fence the side along the river, what is the largest are that can be enclosed? ... ?

The 2 widths make 2x

The length is (7000 - 2x) (not just x)

Area = (7000 - 2x) * x

Area = 7000x - 2x^2

Area = - 2 (x^2 - 1,400x)

Area = - 2 (x^2 - 1,400x + (1,400 / 2) ^2) + 7812.5

Area = - 2 (x - 62.6) ^2 + 7812.5

The maximum area = 7812.5

when

the width = 62.5 and

the length = 250 - 2*62.6

the length = 250 - 125

the length = 125