The perimeter of a rectangular fence is to be at least 92 feet and no more than 130 feet. if the width of the fence is the 30 feet, what is the range of values for the length of the fence?

       To find the range of the length of the fence, form the inequality for the perimeter first then solve the inequality.

   Range of the length of the fence will be between 16 to 35 feet.

Since, perimeter of a rectangular fence is defined as,

 Perimeter = 2(length + width)

And the range of the perimeter is between 92 to 130 feet.

Therefore, inequality defining the range of the perimeter will be,

92 < 2(length + width) < 130

46 < length + width < 65

If the length of the fence = 30 feet

46 < 30 + width < 65

46 - 30 < width < 65 - 30

16 < width < 35

    Therefore, width of the rectangular fence will range between 16 to 35 feet.

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16 to 35

Step-by-step explanation:

The width accounts for two sides of the fence, so we'll double it. 30 × 2 = 60

Now, to find minimum length subtract 60 from 92 and divide by 2 (for each side).

(92 - 60) ÷ 2 = 16

Do the same for the maximum length, but with 130.

(130 - 60) ÷ 2 = 35

This means the range for the length of the fence is between 16 and 35.