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First, let's translate the statement into an inequality. 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. In this case, we are given that the length is 30 centimeters and the perimeter must be no greater than 70 centimeters.
So, we have the inequality:
2(30 + w) ≤ 70
Next, simplify the inequality:
60 + 2w ≤ 70
Subtract 60 from both sides:
2w ≤ 10
Finally, divide both sides by 2 to solve for w:
w ≤ 5
Therefore, the maximum width of the rectangle is 5 centimeters.