The perimeter of a rectangle is to be no greater than 150 centimeters and the length must be 45 centimeters. Find the maximum width of the rectangle.
First, understand the problem. Then translate the statement into an inequality.
The problem states that the perimeter of the rectangle should be no greater than 150 centimeters and the length of the rectangle is 45 centimeters. We need to find the maximum width of the rectangle.
Let's denote the width of the rectangle as "w".
The perimeter of a rectangle is calculated by adding the lengths of all its sides.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Given that the length of the rectangle is 45 centimeters and the perimeter should be no greater than 150 centimeters, we can write the following inequality:
2(45 + w) ≤ 150
Simplifying the inequality:
90 + 2w ≤ 150
Subtracting 90 from both sides:
2w ≤ 60
Dividing both sides by 2:
w ≤ 30
Therefore, the maximum width of the rectangle is 30 centimeters.