The problem states that the perimeter of a rectangle is to be no greater than 60 cm, and the length of the rectangle is fixed at 25 cm. We need to find the maximum possible width of the rectangle.

Step 1: Understand the formula for the perimeter of a rectangle

The perimeter $P$ of a rectangle is given by the formula: $P = 2(\text{length} + \text{width})$ In this case, the length is $25$ cm and the width is $x$ cm.

Step 2: Translate the statement into an inequality

We are told that the perimeter must be less than or equal to 60 cm, so the inequality becomes: $2(25 + x) \leq 60$

Step 3: Solve the inequality

Let's solve for $x$ (the width):

1. Expand the equation: $50 + 2x \leq 60$

2. Subtract 50 from both sides: $2x \leq 10$

3. Divide both sides by 2: $x \leq 5$

Conclusion:

The maximum width of the rectangle is $5$ cm.

Would you like more details on the steps or further clarifications?

Here are 5 related questions you might find useful:

1. What would happen if the perimeter were set to a different value?
2. How would the formula change if the width were fixed instead of the length?
3. What is the area of the rectangle with maximum width?
4. How would you find the width if both perimeter and area constraints were given?
5. What is the smallest possible width for this rectangle?

Tip: When working with perimeter or area, always check the formula and constraints carefully before solving!