Given information:
- The length of a plot is twice its breadth.
- The area of the plot is 4050 square meters.

To find:
- Length and breadth of the plot.

Solution:

Let's assume the breadth of the plot as 'x' meters. According to the given information, the length of the plot would be twice the breadth, so the length can be represented as '2x' meters.

1. Understanding the area:
The area of a rectangle is given by the formula: Area = length * breadth. In this case, the area of the plot is given as 4050 square meters. We can use this information to create an equation.

Area = 4050 square meters
Length * Breadth = 4050

2. Substituting values:
We can substitute the values of length and breadth in the equation:

(2x) * x = 4050

Simplifying the equation further:

2x^2 = 4050

3. Solving the equation:
To find the values of length and breadth, we need to solve the quadratic equation. Let's solve it using factorization method:

2x^2 = 4050
x^2 = 4050/2
x^2 = 2025
x = √2025
x = 45

4. Calculating length:
Now that we have the value of breadth as 45 meters, we can find the length:

Length = 2x
Length = 2 * 45
Length = 90

5. Final answer:
The length of the plot is 90 meters and the breadth is 45 meters.

Summary:
- The breadth of the plot is 45 meters.
- The length of the plot is 90 meters.
- The area of the plot is 4050 square meters.
- The length is twice the breadth, as given in the problem statement.
- By solving the quadratic equation, we found the values of length and breadth.