A rectangular field along a river is to be fenced with 800 f

A rectangular field along a river is to be fenced with 800 feet of fencing. Find the dimension of the field which will produce a maximum area

let length of field be l and width = w

the perimeter of fileld that is to be fenced will have 3 sides

so we can write the equation

l + 2w = 800

l = 800 - 2w

area of filed = length * width

A = lw

plugging the value of l into area equation

A = (800 - 2w ) w

A = 800 w - 2w^2

maximum area occurs at w = -800 / -4 = 200

so width = 200 feet

length = 400 feet