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2006-08-21 01:31:19 · 5 answers · asked by fathom_2005 j 1 in Science & Mathematics ➔ Physics
It should be square. Divide the total fence length available by 4, then square it.
If you have 200 ft of fence, each side will be 50 ft, and the area will be 50*50=2500 square ft.
Additional note: As GreenNGreen says, the best area/perimeter ratio is given for a circle. But for a rectangle, the best shape is a square. (A square is a special case of a rectangle, in other words, all qsquares are also rectangles, but not the other way around.)
2006-08-21 01:37:08 · answer #1 · answered by nitro2k01 3 · 0⤊ 0⤋
Given that the length of the fence is a constant C and the sides are a and b
2a + 2b = C
and the area = ab
define the Area in terms of one of the sides so that
Area = (C/2 - a)a
Area = Ca/2 - a^2
take the derivative and set to zero to find the max or min
C/2 - 2a = 0 so a = C/4 then b must be C/4 as well so the answer is a = b = C/4 or a square.
2006-08-21 02:21:46 · answer #2 · answered by rscanner 6 · 0⤊ 0⤋
L = length W = width 2L + 2W = one hundred meters L + W = 50 or L = 50-W section = L*W section = W(50-W) = 50 W - W^2 darea/dW = 50 - 2W to detect a min or max set spinoff to 0. 50 -2W = 0 or W = 25 then L+W = 50 so L = 25 length =Width =25 meters
2016-11-26 21:10:18 · answer #3 · answered by freije 4 · 0⤊ 0⤋
You specified the shape yourself by saying it is a rectuangular plot. However a rectangle is not ideal in terms of perimeter/area ratio.
The best ratio is obtained when the shape is "Circular".
2006-08-21 01:39:20 · answer #4 · answered by GreenNGreen 1 · 0⤊ 0⤋
The shape of a 'rectangular' plot can only be 'rectangular'.
2006-08-21 01:44:42 · answer #5 · answered by Tim C 4 · 0⤊ 0⤋