The perimeter of a square below is 116 centimeters. The length of a side is 3x + 2.

Find the value of x.

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.

Discover how to find the value of x in a square perimeter problem where the perimeter is 116 centimeters and the side length is expressed as 3x + 2. Follow a step-by-step solution methodically solving for x using basic geometry and algebra. Suitable for Grades 7-9 students.

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