A farmer has 2700 feet of fencing available to enclose a rectangular area bordering a river. if no fencing is required along the river, find the dimensions of the fence that will maximize the area. what is the maximum area

Let L and W be the length and width of the rectangular respectively. Also, let the river run along L.

Perimeter to be covered by fence: P (=2700) = L+2W. Therefore, L=2700-2W

Area, A = LW = (2700-2W) W = 2700W-2W^2. This is quadratic equation.

Now, vertex of the rectangular at maximum area will give maximum width.

This is given by, (W, A), where W = - b/2a where b=2700 and a=-2

Solving for W, W=-2700/2*-2 = - 2700/-4 = 675 ft.

L = 2700-2W = 2700 - 2*675 = 1350 ft

Maximum area, A=1350*675 = 911250 ft^2