To solve for $x$, we start by using the formula for the perimeter of a square:

$\text{Perimeter} = 4 \times \text{side length}$

Given:

• The perimeter is 116 centimeters.
• The length of a side is $3x + 2$.

Using the formula:

$4 \times (3x + 2) = 116$

Now, solve for $x$:

1. Distribute the 4 on the left side:

$12x + 8 = 116$

2. Subtract 8 from both sides:

$12x = 108$

3. Divide by 12:

$x = 9$

So, the value of $x$ is 9.

Would you like more details, or do you have any questions?

Here are some related questions:

1. What would the side length be when $x = 9$?
2. How would the problem change if the perimeter was given instead as 200 centimeters?
3. What is the area of the square when $x = 9$?
4. How do you solve for $x$ if the side length is expressed as $5x - 1$?
5. What would the perimeter be if the side length is doubled?

Tip: Always check your solution by substituting the value of $x$ back into the original equation.