Assessment Practice 12. Jerry built a table with a square top. The perimeter of the tabletop is 18 feet. He knows that the side length of the table is \( 3,3 \frac{1}{4}, 4 \), or \( 4 \frac{1}{2} \) feet. Use the equation \( 18 \boxminus 4 s \), where \( s \) is the side length of the table, to determine the side length of the tabletop. Explain how you found your answer.

To find the side length of Jerry's square tabletop, we start with the known condition that the perimeter of the tabletop is 18 feet. The formula for the perimeter \( P \) of a square is given by: \[ P = 4s \] where \( s \) is the side length of the square. In this case, we can set up the equation: \[ 4s = 18 \] To find \( s \), we can rearrange the equation: \[ s = \frac{18}{4} \] Now, let's simplify this fraction: \[ s = \frac{18 \div 2}{4 \div 2} = \frac{9}{2} = 4.5 \] Now, we need to check if this value matches any of the given options for the side length, which are \( 3, 3 \frac{1}{4}, 4, \) or \( 4 \frac{1}{2} \) feet. The value \( 4.5 \) feet can be expressed as \( 4 \frac{1}{2} \) feet. Thus, the side length of the tabletop is: \[ s = 4 \frac{1}{2} \text{ feet} \] ### Explanation of the Steps: 1. **Identify the formula for the perimeter of a square**: We used the formula \( P = 4s \). 2. **Set up the equation**: We substituted the known perimeter (18 feet) into the formula. 3. **Solve for \( s \)**: We rearranged the equation to isolate \( s \) and calculated its value. 4. **Match with given options**: We compared the calculated side length with the provided options to find the correct one. Therefore, the side length of the tabletop is \( 4 \frac{1}{2} \) feet.