The perimeter of a rectangle is to be no greater than 70 centimeters and the length must be 30 centimeters. Find the maximum width of the rectangle.
First, understand the problem. Then translate the statement into an inequality.
the perimeter of the rectangle x+30+blank
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.