My rectangular soccer field site has a length equal to one and a half times its width. Find its area in terms of its length x.

Let the width of the rectangular soccer field be denoted by \( w \), and the length by \( x \). According to the problem, the length is one and a half times the width:

\[
x = \frac{3}{2} w
\]

To express the width in terms of the length \( x \), solve for \( w \):

\[
w = \frac{2}{3} x
\]

The area \( A \) of the rectangular soccer field is given by the product of the length and width:

\[
A = x \times w
\]

Substituting \( w = \frac{2}{3} x \) into the equation for area:

\[
A = x \times \frac{2}{3} x = \frac{2}{3} x^2
\]

Thus, the area of the soccer field in terms of its length \( x \) is:

\[
A = \frac{2}{3} x^2
\]

Would you like more details or have any questions about this? Here are some related questions for further exploration:

1. What is the width of the field if the length is 90 meters?
2. How would the area formula change if the length were twice the width?
3. What is the perimeter of the field in terms of \( x \)?
4. If the area is 5400 square meters, what is the length of the field?
5. How would the area change if the length were increased by 20%?

**Tip:** When working with ratios, always solve for one variable in terms of the other to make calculations easier.

Discover how to calculate the area of a rectangular soccer field where the length is 1.5 times the width. This problem involves basic geometric and algebraic concepts suitable for students in Grades 6-8.

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