The dimension of the pool has a length of 27.5 feet and width of 27.5 feet.
Let x represent the length of the pool and y represent the width of the pool
Perimeter = 2(length + width)
110 = 2(x + y)
x + y = 55
y = 55 - x
Area (A) = length * width
A = x * y
A = x(55 - x)
A = 55x - x²
The maximum area is at dA/dx = 0, hence:
dA/dx = 55 - 2x
0 = 55 - 2x
2x = 55
x = 27.5 feet
y = 55 - x = 55 - 27.5
y = 27.5 feet
The dimension of the pool has a length of 27.5 feet and width of 27.5 feet.
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