Let the width of the rectangular soccer field be $w$. According to the problem, the length of the field is three times its width, so the length is given by:

$L = 3w$

Since the area $A$ of a rectangle is given by:

$A = L \times w$

Substitute $L = 3w$ into the area formula:

$A = 3w \times w = 3w^2$

Now, if the length is denoted as $x$, we know that $x = 3w$. Solving for $w$:

$w = \frac{x}{3}$

Substitute this expression for $w$ into the area formula:

$A = 3 \left( \frac{x}{3} \right)^2$

Simplify the expression:

$A = 3 \times \frac{x^2}{9} = \frac{x^2}{3}$

Thus, the area $A$ in terms of the length $x$ is:

$A = \frac{x^2}{3}$

Let me know if you'd like more details or have any questions!

Here are 5 related questions:

1. What is the width of the field if the length is 90 meters?
2. How does the formula change if the length is four times the width instead of three?
3. If the area is 600 square meters, what is the length of the field?
4. How would the area change if both the length and width were doubled?
5. What would the perimeter of the soccer field be in terms of $x$?

Tip: Always label your dimensions clearly when working with geometric shapes!