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26 May, 14:40

Lucy bought 162 feet of fencing with which to enclose a rectangular garden. of the lengths of the garden's sides are whole numbers, what is the maximum number of square feet she can enclose with the fencing?

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  1. 26 May, 14:45
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    The maximum area would be a square so we need the length and width to be as close as possible to a square. The perimeter is 162 so we have:-

    2L + 2W = 162

    L + W = 81

    so the length will be 41 and width will be 40

    So greatest area she can enclose = 40*41 = 1640 ft^2
  2. 26 May, 14:47
    0
    The rectangle that uses it's perimeter to enclose the most area is a square.

    If the perimeter is 162 ft, then each side of the square is

    162 / 4 = 40.5 ft.

    The area is

    (40.5) x (40.5) = 1,640.25 square feet.

    If the sides have to be whole numbers, then the closest she can get is 40 ft x 41 ft.

    The area is 1,640 square feet.
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