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7 August, 00:53

John wants to build a corral next to his barn. He has 300 feet of fencing to enclose three sides of his rectangular yard.

a. What is the largest area that can be enclosed?

b. What dimensions will result in the largest yard?

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  1. 7 August, 02:21
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    Let's first define the variables:

    x = width

    300 - 2x = long

    The area will be:

    A = (x) * (300 - 2x)

    A = 300x - 2x²

    We look for the maximum area, for this, we derive:

    A ' = 300 - 4x

    We match zero:

    0 = 300 - 4x

    x = 300/4 = 75

    Therefore, the width is:

    x = 75 feet

    The length is:

    300 - 2x = 300 - 2 (75) = 300-150

    150 feet

    Answer:

    Part A:

    The maximum area will be:

    A = (150) * (75) = 11250 square feet

    Part B:

    The dimensions are:

    Length = 150 feet

    width = 75 feet
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