Let the length of one side of the rectangle be $x$, and the other side be $y$. The perimeter of a rectangle is given by:

$P = 2x + 2y$

Since the perimeter is 12 m, we can write:

$2x + 2y = 12$

Simplifying, we get:

$x + y = 6$

Now, express $y$ in terms of $x$:

$y = 6 - x$

The area $A$ of a rectangle is the product of its length and width, so:

$A(x) = x \cdot y = x \cdot (6 - x)$

Therefore, the area as a function of $x$ is:

$A(x) = 6x - x^2$

This is the required expression for the area in terms of the length of one side $x$.

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:

1. What value of $x$ maximizes the area of the rectangle?
2. How does the area change if the perimeter is doubled?
3. What is the area when $x = 3$?
4. How would the formula change if the perimeter were 20 m instead of 12 m?
5. Can you find the dimensions of the rectangle when the area is maximized?

Tip: For problems involving the perimeter of a rectangle, try simplifying the equation early to express one side in terms of the other.