Question

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

Answer 1

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

Answer 2

rectangular field width is ( 675 feet ) and length ( 1350 feet ) solution is attached