To solve this problem, let's first use the given formula for the perimeter of a square, which is:

$P = 4s$

where $P$ is the perimeter and $s$ is the length of a side.

The problem states that the perimeter $P$ is equal to 6 times the length of a side decreased by 6. So, we can write this as:

$P = 6s - 6$

Now, we have two expressions for the perimeter:

1. $P = 4s$ (the formula for the perimeter of a square)
2. $P = 6s - 6$ (the condition given in the problem)

Since both represent the same perimeter, we can set them equal to each other:

$4s = 6s - 6$

Now, solve for $s$: $4s - 6s = -6$ $-2s = -6$ $s = \frac{-6}{-2} = 3$

Thus, the length of a side is 3.

The correct answer is C.

Would you like further explanation or have additional questions on this topic?

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Follow-up questions:

1. How would the perimeter change if the side length were doubled?
2. Can the formula for the perimeter be modified for non-square polygons?
3. What is the area of the square with side length 3?
4. How do you solve for the side length if the perimeter was expressed differently (e.g., in terms of a different equation)?
5. What happens to the perimeter if we increase the side length by 1 unit?

Tip: Always write down your equations clearly and identify all variables before solving, as it helps prevent mistakes.