The dimensions of the rectangular enclosure for his garden is length of 7.5 m and width of 7.5 m.
Let x represent the length of the garden and y represent the width of the garden.
Perimeter = 2(x + y)
30 = 2(x + y)
x + y = 15
y = 15 - x
Area (A) = length * width
A = xy
A = x(15 - x)
A = 15x - x²
Maximum area is at dA/dx = 0:
dA/dx = 15 - 2x
0 = 15 - 2x
2x = 15
x = 7.5 m
y = 15 - x = 15 - 7.5 = 7.5 m
The dimensions of the rectangular enclosure for his garden is length of 7.5 m and width of 7.5 m.
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