We are given that:

1. The length of the rectangle is 2 inches less than 3 times the width. This can be expressed as: $\text{Length} = 3w - 2$ where $w$ is the width of the rectangle.

2. The area of the rectangle is given by 225 square inches. The area of a rectangle is calculated as the product of its length and width: $\text{Area} = \text{Length} \times \text{Width}$ Substituting the known values: $225 = (3w - 2) \times w$

This equation represents the relationship between the width $w$ and the area of the rectangle.

To expand and simplify: $225 = (3w - 2)w$ $225 = 3w^2 - 2w$

Thus, the equation describing the relationship between $w$ and the area is: $3w^2 - 2w - 225 = 0$

Would you like me to solve this quadratic equation? Let me know if you'd like further details or have any questions!

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Here are some related questions to explore:

1. How would you solve the quadratic equation $3w^2 - 2w - 225 = 0$ using the quadratic formula?
2. What are some real-world applications of quadratic equations in geometry?
3. How can you verify the solution for the width of the rectangle?
4. What is the relationship between the width and length if the area changes?
5. How would the equation change if the length were 5 inches less than 4 times the width?

Tip: To solve quadratic equations like this, try factoring first. If factoring is difficult, the quadratic formula is a reliable method.