To find the length of one side of a regular octagon, we can use the formula for the perimeter of a regular polygon:

$\text{Perimeter} = \text{Number of sides} \times \text{Length of one side}$

Given that the perimeter of the octagon is 136 cm and it has 8 sides (since it's an octagon), we can set up the equation:

$136 = 8 \times \text{Length of one side}$

Now, solve for the length of one side:

$\text{Length of one side} = \frac{136}{8} = 17 \, \text{cm}$

Thus, the length of one side of the regular octagon is 17 cm.

Would you like further clarification or have any other questions? Here are some related questions for further practice:

1. What is the area of a regular octagon with a side length of 17 cm?
2. How does the perimeter of a regular polygon change if the number of sides increases?
3. How do you calculate the interior angle of a regular octagon?
4. How do you find the radius of the circumcircle of a regular octagon?
5. What would the perimeter of the octagon be if the side length was 20 cm instead?

Tip: When working with regular polygons, the relationship between the number of sides and the perimeter is straightforward. Make sure to always identify how many sides the polygon has before using the perimeter formula!