You are marking a rectangular paintball zone that must be 34 meters wide and have a perimeter of at least 140 meters but not more than 260 meters. Find the interval for the length $x$ of the rectangular paintball zone. Write your answer in interval notation.

36m <= L <= 96m

Explanation:

Since the paintball is rectangular, the formula for the perimeter P of a rectangle is:

P = 2(L + B)

Where L = length

B = width

Given that the rectangular paintball zone must be 34 meters wide and have a perimeter of at least 140 meters but not more than 260 meters. 

When the perimeter is least, the length will be achieved by substituting the perimeter and the width into the formula. That is,

140 = 2(L + 34)

L + 34 = 140/2

L = 70 - 34

L = 36m

When the perimeter is maximum, that is, 260m. Substitute it and the width into the formula

260 = 2(L + 34)

L + 34 = 260/2

L + 34 = 130

L = 130 - 34

L = 96.

Therefore, the interval for the length of the rectangular paintball zone will be:

36m to 96m. That is

36m <= L <= 96m

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