To find the perimeter of a rectangle, we need both the length ($l$) and the width ($w$) of the rectangle. Since we are given only the area, which is $\text{Area} = l \times w = 24 \, \text{cm}^2$, we do not have enough information to uniquely determine the dimensions of the rectangle and hence the perimeter.

However, we can express the perimeter ($P$) in terms of $l$ and $w$: $P = 2(l + w).$

Since $l \times w = 24$, you can choose various pairs of factors of 24 (e.g., $l = 6, w = 4$ or $l = 8, w = 3$), calculate the corresponding perimeter, and observe that the perimeter will vary depending on the chosen dimensions.

Example 1: $l = 6$, $w = 4$

$P = 2(6 + 4) = 20 \, \text{cm}.$

Example 2: $l = 8$, $w = 3$

$P = 2(8 + 3) = 22 \, \text{cm}.$

Without additional constraints, the perimeter cannot be uniquely determined. If you provide further information (e.g., one side length, or that it’s a square), we can refine the answer.

Would you like more examples or additional explanations?

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Related Questions:

1. How does the area relate to the dimensions of a rectangle?
2. If one side length of the rectangle is known, how do you find the other side?
3. How do you calculate the diagonal of a rectangle given its area and perimeter?
4. What are the implications of assuming the rectangle is a square?
5. How does changing the length-to-width ratio affect the perimeter for a fixed area?

Tip: For rectangles with fixed area, the square configuration always minimizes the perimeter.