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Explain why the perimeter:Area ratio value can be used to understand cost effectiveness

  • Math -

    perimeter defines the length and therefore cost of fencing.
    area defines the size of the enclosure, for example how much grass for the cows to munch.
    the minimum fence length for maximum grass is the perimeter to area ratio.
    Example for rectangle:
    What are the dimensions of a rectangular field that surrounds the maximum area with 100 meters of fence?
    x+y = 50
    A = x y

    if it is square:
    25 on a side
    area = 625


    if one side is longer, for example 10 by 40
    area = 400

    least fence cost for square, x/y = 1
    perimeter/area = 4 x/x^2 = 4/x

  • Math -

    to find the total area under sq.feet

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