You have a 1800 foot roll of fencing. You are going to enclose a rectangular field. You want to place a row of fence down the middle to divide it into two equal sections. What is the maximum area you can enclose?
1 Answer
Sep 27, 2017
The perimeter will be given by
#2x+ 3y = 1800#
Because we need three lengths and two widths.
Hence, we can say
#3y = 1800- 2x#
#y = 600 - 2/3x#
Using
#A = (600 - 2/3x)x#
#A = 600x - 2/3x^2#
Completing the square to get the vertex:
#A = -2/3(x^2 - 900x + 202500 - 202500)#
#A = -2/3(x^2 - 900x + 202500) + 135000#
#A = -2/3(x - 450)^2 + 135000#
So the maximum area is
Hopefully this helps!