A square piece of paper is folded in half tomake a rectangle. The perimeter of therectangle is 24.9 cm. What is the side lengthof the square piece of paper?

1. Break Down the Problem

• We have a square piece of paper.
• When folded in half, it forms a rectangle.
• The perimeter of the rectangle is given as 24.9 cm.
• We need to find the side length of the original square piece of paper.

2. Relevant Concepts

• Let the side length of the square be $s$.
• When folded in half, the width of the rectangle will be $\frac{s}{2}$ and the height will be $s$.
• The perimeter $P$ of a rectangle is given by the formula: $P = 2 \times (\text{length} + \text{width})$

3. Analysis and Detail

• Given the width ($w$) and height ($h$) of the rectangle, we have: $w = \frac{s}{2}, \quad h = s$
• Substituting these into the perimeter formula: $P = 2 \times \left(s + \frac{s}{2}\right)$
• Simplifying the equation: $P = 2 \times \left(\frac{3s}{2}\right) = 3s$
• Setting the perimeter equal to 24.9 cm: $3s = 24.9$

4. Verify and Summarize

• To find $s$, divide both sides by 3: $s = \frac{24.9}{3} = 8.3$
• So, the side length of the square piece of paper is 8.3 cm.

Final Answer

The side length of the square piece of paper is 8.3 cm.