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11 April, 17:22

Emily is creating a rectangular garden in her backyard. The length of the garden is 12 feet. The perimeter of the garden must be at least 30 feet and no more than 64 feet. Use a compound inequality to find the range of values for the width w of the garden

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  1. 11 April, 17:30
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    w ≥ 3 AND w ≤ 20

    Step-by-step explanation:

    1. Let's review the information given to us to answer the question correctly:

    Length of Emily's garden = 12 feet

    Perimeter of Emily's garden should be at least 30 feet and no more than 64 feet

    2. Use a compound inequality to find the range of values for the width w of the garden

    Let's recall the perimeter formula of a rectangle:

    Perimeter = 2 * Length + 2 * Width

    Replacing the values we know:

    30 = 2 * 12 + 2 Width

    30 = 24 + 2 Width

    30 - 24 = 2 Width

    6 = 2 Width

    6/2 = Width

    Width = 3 feet

    For having a 30 feet perimeter, we should have a 3 feet width. Now, let's calculate the width for a 64 feet perimeter, using the same formula:

    64 = 2 * 12 + 2 Width

    64 = 24 + 2 Width

    64 - 24 = 2 Width

    40 = 2 Width

    40/2 = Width

    Width = 20 feet

    For having a 64 feet perimeter, we should have a 20 feet width. Now, let's write our compound inequality:

    w ≥ 3 AND w ≤ 20
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