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11 August, 05:15

What is the difference between the greatest and least possible area of the rectangle when the parameter of 18 inches

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  1. 11 August, 08:06
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    If the perimeter is fixed and you want to use it to enclose the greatest

    possible area, then you form the perimeter that you have into a circle.

    If it must be a rectangle, then the greatest possible area you can enclose

    with the perimeter that you have is to form it into a square.

    Since the perimeter that you have is 18 inches, form it into a square

    with sides that are 4.5 inches long.

    The area of the square is (4.5) ² = 20.25 square inches.

    There is no such thing as the 'least possible' area of the rectangle.

    The longer and skinnier you make it, the less area it will have, even

    if you keep the same perimeter. No matter how small you make the

    area, it can always be made even smaller, by making the rectangle

    even longer and skinnier. You can make the area as small as you

    want it. You just can't make it zero.

    Example:

    Width = 0.0001 inch

    Length = 8.9999 inches

    Perimeter = 18 inches

    Area = 0.00089999 square inch.

    So, the difference between the greatest and least possible area

    of the rectangle with the perimeter of 18 inches is

    (20.25) - (the smallest positive number you can think of) square inches.
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