In the given problem, we are dealing with a regular hexagon, meaning all its sides are of equal length. The perimeter of the hexagon is given as 108 cm, and the expression for each side is $x + 7$.

Step 1: Write the equation for the perimeter.

Since a hexagon has 6 sides, the perimeter (the sum of all side lengths) can be expressed as: $\text{Perimeter} = 6 \times (\text{Side length})$

In this case, the side length is $x + 7$, so the perimeter equation becomes: $6 \times (x + 7) = 108$

Step 2: Solve the equation.

Now, solve for $x$:

$6(x + 7) = 108$

First, distribute the 6 on the left side: $6x + 42 = 108$

Next, subtract 42 from both sides: $6x = 108 - 42$ $6x = 66$

Now, divide both sides by 6: $x = \frac{66}{6}$ $x = 11$

Final Answer:

The value of $x$ is 11.

Would you like further explanations or have any questions about the process?

Here are some related questions:

1. How do you calculate the perimeter of other polygons with given side expressions?
2. How does this approach change if the hexagon is not regular?
3. What is the relationship between the side length and the perimeter in regular polygons?
4. Can you generalize the perimeter equation for polygons with any number of sides?
5. How does changing the value of $x$ affect the perimeter of the hexagon?

Tip: Always check the number of sides of the polygon when calculating perimeter, as it will directly affect the equation.