Farmer ed has 550 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, find the length and width of the plot that will maximize the area. what is the largest area that can be enclosed?

Let width of the rectangular plot be x meters

then total of widths = 2x 
and the length would be (550 - 2x) meters.

so the area = x(550 - 2x)  = 550x - 2x^2

to find the maximum are find the derivative and equate to zero:-

f'(x) =  550 - 4x = 0
x = 550/4 =  137.5 meters = width

length = 550 - 2(137.5) = 275

Maximum area  is when width = 137.5m and length = 275m