Question 720082
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground.
 472 feet of fencing is used.
 Find the dimensions of the playground that maximize the total enclosed area.
:
Normally the perimeter would be 2L + 2W but since we have one more side to divide the area we will write it:
2L + 3W = 472
divide by 2
L + 1.5W = 236
then
L = (236-1.5w)
:
The area: A = L * W
replace L with (236-1.5W)
A = W(236-1.5W)
A = -1.5W^2 + 236W
This is a quadratic equation, if we find the axis of symmetry, we will know the value of W that gives max area. 
Formula for the axis of symmetry: x = -b/2a, in this problem it would be
W = -236/(2*-1.5)
W = -236/-3
W = +78{{{2/3}}} ft is the width
Find the Length
L = 236 - 1.5(78.667)
L = 159{{{1/3}}} is the length for max area