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12 April, 15:16

Mike wants to fence in part of his backyard. He wants the length of the fenced-in area to be at least 20 feet long, l ≥ 20. He has 200 feet of fencing. The inequality that models the possible perimeter of the yard is 2l + 2w ≤ 200.

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  1. 12 April, 15:55
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    Answers:

    w = 10 ft and l = 50 ft ... > second option

    w = 20 ft and l = 60 ft ... > third option

    w = 50 ft and l = 40 ft ... > fifth option

    Explanation:

    We are given that:

    length should be at least 20 ... > length ≥ 20

    equation for perimeter is : 2l + 2w ≤ 200

    We will check each option as follows:

    Option 1:

    w = 50 ft and l = 10 ft

    This option is incorrect as the proposed length is less than 20.

    Option 2:

    w = 10 ft and l = 50 ft

    Since the length is greater than 20, the first condition is satisfied.

    Now, we check the second condition:

    2l + 2w = 2 (50) + 2 (10) = 100 + 20 = 120 ≤ 200

    The second condition is also satisfied.

    This option is correct

    Option 3:

    w = 20 ft and l = 60 ft

    Since the length is greater than 20, the first condition is satisfied.

    Now, we check the second condition:

    2l + 2w = 2 (60) + 2 (20) = 120 + 40 = 160 ≤ 200

    The second condition is also satisfied.

    This option is correct

    Option 4:

    w = 90 ft and l = 30 ft

    Since the length is greater than 20, the first condition is satisfied.

    Now, we check the second condition:

    2l + 2w = 2 (30) + 2 (90) = 60 + 180 = 240 > 200

    The second condition is not satisfied.

    This option is incorrect

    Option 5:

    w = 50 ft and l = 40 ft

    Since the length is greater than 20, the first condition is satisfied.

    Now, we check the second condition:

    2l + 2w = 2 (50) + 2 (40) = 100 + 80 = 180 ≤ 200

    The second condition is also satisfied.

    This option is correct
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