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Suppose you have 100ft of fence to make a play area for your dog. Does a square or circle provide more area? What other factors might you take into consideration in designing your play area?

  • Math -

    The circle is the most efficient shape for a maximum area given some perimeter.
    Here is why:
    if circumf = 100
    2πr = 100
    r = 100/(2π) = 15.915
    area = πr^2 = π(15.915)^2 = 795.77

    if you had a square:
    each side = 25
    Area = 25x25 = 625 which is quite a bit less than the circle
    Any other shape, e.g. an equilateral triangle, is less than the area of a circle.

  • Math -

    Circle it has a larger area by 3 more

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