The maximum area has a length of 40 feet and a width of 40 feet
Let x represent the length of the garden and y represent the width of the garden.
Since the length of the fence is 150 feet and there is a 10 feet opening, hence:
Perimeter of garden = 2(x + y)
2(x + y) = 150 + 10
2(x + y) = 160
x + y = 80
y = 80 - x
Area (A) = xy = x(80 - x)
A = 80x - x²
The maximum area is at dA/dx = 0, hence:
dA/dx = 80 - 2x
80 - 2x = 0
2x = 80
x = 40 feet
y = 80 - x = 80 - 40
y = 40 feet
Hence the maximum area has a length of 40 feet and a width of 40 feet
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