Answer:
Explanation:
You want the length and width of a garden that will require the least fence for a 24 ft² area if the length is one of 6 ft, 8 ft, or 12 ft.
Width
The area is the product of length and width, so we have ...
A = LW
A/L = W
The width is the 24 ft² area divided by the length.
Perimeter
The perimeter is the sum of the sides of the rectangular garden. There are two sides of the chosen length, and two of the corresponding width, so the perimeter is ...
P = 2(L +W)
These relations are used in the attached calculation to find the perimeter for each of the given lengths.
- length 6 ft — perimeter 20 ft . . . . . least fence
- length 8 ft — perimeter 22 ft
- length 12 ft — perimeter 28 ft
The dimensions requiring the least fence are ...
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Additional comment
The absolute least amount of fence is required when the garden is square. The closer to square it is, the less fence is used. The dimensions of a square garden would be √24 ≈ 4.90 ft, so the nearest choice is 6 ft.
The square garden would require 19.6 ft of fence, so the 6 ft × 4 ft garden is near the optimum.