600 feet of fencing to enclose a rectangular plot

If I don't fence one side what is the length and width of the plot that maximized the area?

1 answer

it is useful to know that a square is the figure of maximum area for a given perimeter.

Similarly, a cube is the figure of maximum volume for a given surface area.

Formally, if the width is x, then the length is (600-2x)/2 = 300-x

So, the area is given by

a = x(300-x) = 300x-x^2
da/dx = 300-2x
da/dx=0 at x = 150
so, the rectangle is 150x150