To solve this problem, we first need to identify the dimensions of the rectangle based on the information given in the image:

1. Width of the rectangle: $x$
2. Length of the rectangle: $3x - 1$
3. Area of the rectangle: $184 \, m^2$

The area $A$ of a rectangle is calculated by multiplying its length and width: $A = \text{length} \times \text{width}$

Substituting the given values into this formula: $184 = x \times (3x - 1)$

To find the equation that allows us to determine the dimensions of the rectangle, we expand and set the equation to zero: $184 = 3x^2 - x$

Rearranging it gives: $3x^2 - x - 184 = 0$

This is a quadratic equation. Solving this equation will give us the value of $x$ and, subsequently, the dimensions of the rectangle.

Would you like to solve this quadratic equation for $x$?

Additional Questions:

1. What is the value of $x$ when solving the quadratic equation $3x^2 - x - 184 = 0$?
2. How do you calculate the area of a rectangle given its length and width?
3. What methods can be used to solve quadratic equations?
4. What are the properties of rectangles that distinguish them from other quadrilaterals?
5. How can the concept of area be applied in real-life scenarios?

Tip:

When solving quadratic equations, always check if it can be factored easily, otherwise use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.$