Final answer:
To solve this problem, set up an equation based on the given information: 28 ≥ 2((x-2)² + x). Simplify and solve for x: x ≤ -2 or x ≥ 5. Since the width cannot be negative, the width of the table should be ≥ 5 feet.
Step-by-step explanation:
To solve this problem, we need to set up an equation based on the given information. Let's say the width of the table is x feet. According to the problem, the length of the table should be greater than or equal to the square of 2 feet less than its width. So, the length would be (x-2)² feet. The perimeter of a rectangle is given by the formula P = 2(l+w), where P is the perimeter, l is the length, and w is the width. We are told that the perimeter should be no more than 28 feet. Plugging in the values, we get: 28 ≥ 2((x-2)² + x). Now, we can simplify the equation and solve for x:
28 ≥ 2(x² - 4x + 4 + x)
28 ≥ 2(x² - 3x + 4)
14 ≥ x² - 3x + 4
x² - 3x - 10 ≤ 0
(x - 5)(x + 2) ≤ 0
The solutions to this inequality are x ≤ -2 or x ≥ 5.