SOLUTION: Bill wants to build a rectangular garden against one side of his house. He bought 240 feet of fence. what is the dimension of the rectangular garden must be to maximize the area?
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Question 1130473: Bill wants to build a rectangular garden against one side of his house. He bought 240 feet of fence. what is the dimension of the rectangular garden must be to maximize the area? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Bill wants to build a rectangular garden against one side of his house.
He bought 240 feet of fence.
what is the dimension of the rectangular garden must be to maximize the area?
:
The perimeter of the fence only, three sides
L + 2w = 240
L = -2w + 240
:
Area
A = L*w
replace L with (-2w+240)
A = w(-2w+240)
A = -2w^2 + 240w
Max area occurs on the axis of symmetry. Find this using formula: x = -b/(2a)
In the above equation a=-2; b=240
w =
w = 60 ft width will give max area
find L
L = -2(60) + 240
L = 120 ft is the length
:
Garden dimensions of 120 by 60 will give max area. (7200sq/ft)
