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11 October, 10:02

a rectangular field is to be enclosed on four sides with a fence. fencing costs 5$ per foot two opposite sides, and 6$ per foot for the other two sides. find the dimensions of the feild of area 710ft

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  1. 11 October, 10:09
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    Length of cheaper side = x = 29.21 ft

    Length of expensive side = y = 24.31 ft

    Step-by-step explanation:

    Let

    Length of cheaper side = x

    Length of expensive side = y

    Total Cost = 5 (x + x) + 6 (y+y) =

    Total Cost = 5 (2x) + 6 (2y)

    Total Cost = 10x + 12y

    we also know that

    xy = 710ft square

    so

    y = 710 ft sq. / x

    Putting this in total cost equation

    Total Cost = 10x + 12 (710 ft sq. / x)

    f (x) = 10x + (8,520 ft sq. / x) (cost = f (x)

    f' (x) = 10 - (8,520 ft / x^2) (x>0)

    0 + (8,520 ft / x^2) = 10

    8,520 ft / x^2 = 10

    x^2 = 8,520 ft / 10

    (x^2) ^1/2 = (8,520 ft / 10) ^1/2

    x = 92.3 / 3.16

    x = 29.21 ft

    As given

    xy = 710ft square

    Putting value of x in above equation

    29.21 y = 710

    y = 710/29.21

    y = 24.31 ft
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