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a rectangular field with an area of 8000 m^2 is enclosed by 400 m of fencing , detemine the dimesions of the field to the nearest tenth of a metre

  • Math -

    first we represent the unknowns using variables:
    let x = length
    let y = width
    recall that perimeter of rectangle is just,
    P = 2x + 2y
    since P is given (which is 400), we can get an expression of width in terms of length:
    400 = 2x + 2y
    400 - 2x = 2y
    y = 200 - x
    then to get the dimensions, we use the area given. recall that area of rectangle is just,
    A = xy
    substituting,
    8000 = x(200 - x)
    8000 = 200x - x^2
    x^2 - 200x + 8000 = 0
    then solve for x using quadratic equation. then also solve for y.

    hope this helps~ :)

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