Define variables for the dimensions of the rectangular plot.

Let $w$ be the width of the plot in meters.
Let $l$ be the length of the plot in meters.

The problem states that the length of the plot is 3 meters more than its width.

The area of a rectangle is given by $A = l \times w$.
The total area is $180 \text{ m}^2$.
Substitute the expressions for $l$ and $A$:

Subtract 180 from both sides:

The quadratic equation is:

We need to find two numbers that multiply to -180 and add up to 3.
These numbers are 15 and -12.

Set each factor equal to zero:

Since width cannot be negative, we discard $w = -15$.
Therefore, the width of the plot is $w = 12 \text{ m}$.

Using the relationship $l = w + 3$:

The dimensions of the plot are: