Question 1129322: Ed is planning to put up a rectangular garden with a fixed area of 120m^2. If the dimension of the garden have to be whole numbers, determine the dimension that will require the least amount of fencing materials to enclose the garden?
Explain with solution.
Answer by greenestamps(13195)   (Show Source):
You can put this solution on YOUR website!
Area is length times width; that has to be 120. Perimeter is twice the sum of length and width; we want that to be a minimum, since the amount of fencing depends on the perimeter.
The possible dimensions x and y, if they have to be whole numbers; and the corresponding perimeters, 2(x+y):
120 by 1; 2(121) = 242
60 by 2; 2(62) = 124
40 by 3; 2(43) = 86
30 by 4; 2(34) = 68
24 by 5; 2(29) = 58
20 by 6; 2(26) = 52
15 by 8; 2(23) = 46
12 by 10; 2(22) = 44
ANSWER: The 12m by 10m garden will require the least amount of fencing.
Note this problem displays a useful general principle: The least perimeter for a rectangle with a given area is with the length and width as close to equal as possible.
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