What is the solution set of the inequality?
1 answer:
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I added a screenshot of the complete question along with the given choices.
<em><u>Answers:</u></em>
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
<em><u>Explanation:</u></em>
<u>We are given that:</u>
length should be at least 20 ...........> length ≥ 20
equation for perimeter is : 2l + 2w ≤ 200
<u>We will check each option as follows:</u>
<u>Option 1:</u>
w = 50 ft and l = 10 ft
This option is incorrect as the proposed length is less than 20.
<u>Option 2:</u>
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
<u>Option 3:</u>
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
<u>Option 4:</u>
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
<u>Option 5:</u>
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
Hope this helps :)
