The dimensions of the fence which would maximize the area are 7.5 feet by 7.5 feet
How to determine the dimensions?
The given parameter is:
Perimeter, P = 30 feet
The perimeter is calculated as:
P = 2 (x + y)
So, we have:
2(x + y) = 30
Divide by 2
x + y = 15
Make x the subject
x = 15 - y
The area is calculated as:
A = xy
Substitute x = 15 - y
A = (15 - y)y
Expand
A = 15y - y^2
Differentiate
A' = 15 - 2y
Set to 0
15 - 2y = 0
Divide through by 2
7.5 - y = 0
Solve for y
y = 7.5
Substitute y = 7.5 in x = 15 - y
x = 15 - 7.5
Evaluate
x = 7.5
Hence, the dimensions of the fence which would maximize the area are 7.5 feet by 7.5 feet
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