The question states that a rectangle has a perimeter of 54 cm and a length of 21 cm, and asks for its width.

To solve this, we use the formula for the perimeter of a rectangle:

$P = 2L + 2W$

Where:

• $P$ is the perimeter,
• $L$ is the length,
• $W$ is the width.

Given that the perimeter $P = 54$ cm and the length $L = 21$ cm, substitute these values into the formula:

$54 = 2(21) + 2W$

Simplify:

$54 = 42 + 2W$

Now, solve for $W$:

$54 - 42 = 2W$

$12 = 2W$

$W = \frac{12}{2} = 6$

Thus, the width of the rectangle is 6 cm.

Would you like a more detailed explanation or any clarifications?

Here are five follow-up questions to deepen your understanding:

1. How would the formula change if you were given the area instead of the perimeter?
2. Can you generalize this process to find the width for any rectangle if only given the perimeter and length?
3. What is the relationship between perimeter and area in a rectangle?
4. How would you solve this if the perimeter was given in inches instead of centimeters?
5. What would happen to the width if the perimeter was doubled but the length stayed the same?

Tip: Always double-check your algebraic steps to avoid small mistakes when isolating variables!