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17 May, 13:57

Find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 300 feet of fencing. (Assume that the length is greater than or equal to the width.) ft length width ft Tutorial Additional Materials eBook Example Video

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  1. 17 May, 14:03
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    Answer:Dimensions are of one corral is:

    Length=50ft

    Width = 37.5ft

    Combined area=1875ft

    Step-by-step explanation:

    Let L = length

    Let w = width

    There are 3 pieces of fencing: 3L + 4w = 300

    W = (300 - 3L) / 4 ... equation 1

    Combined area of the corrals is given by:

    A = L * 2w ... eq2

    Put eq1 into eq2

    A = L * 2 (300-3L) / 4

    A = 1/2 (300 - 3 L) ^2

    A = - (3/2) L^2 + 150

    Using - b/2a to solve for L in the quadratic equation

    -150/2 (3/2) = (150*2) / (2*3)

    L = 50ft

    W = 300-3 (50) / 4

    W=150/4=37.5ft

    Combined are=50*37.5=1875ft
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