Answer:
Step-by-step explanation:
Let y = length of side parallel to the side with no fence
x = length of each of the other two sides
Then, y+2x = 64. So, y = 64-2x
Area = A = xy = x(64-2x)
The graph of the area function is a parabola opening downward with a highest point and with x-intercepts (0,0) and (32,0).
By the symmetry of the parabola, the x-coordinate of the maximum point lies halfway between the x-intercepts.
So, the area is maximized when x = 16 ft
y = 64 - 2x = 32 ft
Maximum area = xy = (16)(32) = 512 ft2
To maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.
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Long N. answered • 10/06/16
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For the fixed given perimeter, the maximum area which can be obtained is a square.
So for 3 sides= 64 feet
one side = 64/3
The maximum area is 64/3*64/3 square feet
