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.

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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.
The side length of the tabletop is $$ 4 \frac{1}{2} $$ feet.

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