Let's define the breadth of the rectangular plot as $b$ meters. According to the problem, the length of the plot is "one meter more than twice its breadth." This can be expressed as:

$\text{Length} = 2b + 1 \, \text{meters}$

The area of a rectangle is given by:

$\text{Area} = \text{Length} \times \text{Breadth}$

Substituting the given area (528 m²) and the expressions for length and breadth into this equation:

$528 = (2b + 1) \times b$

Now, let's solve for $b$ (breadth) by expanding and rearranging the equation:

$528 = 2b^2 + b$

Rearranging the equation:

$2b^2 + b - 528 = 0$

This is a quadratic equation. We'll use the quadratic formula to solve for $b$:

$b = \frac{-1 \pm \sqrt{1^2 - 4(2)(-528)}}{2(2)}$

$b = \frac{-1 \pm \sqrt{1 + 4224}}{4}$

$b = \frac{-1 \pm \sqrt{4225}}{4}$

$b = \frac{-1 \pm 65}{4}$

Taking the positive root (since dimensions cannot be negative):

$b = \frac{-1 + 65}{4} = \frac{64}{4} = 16$

Thus, the breadth $b = 16$ meters.

Now, using the expression for the length:

$\text{Length} = 2b + 1 = 2(16) + 1 = 32 + 1 = 33 \, \text{meters}$

Final Answer:

• Length = 33 meters
• Breadth = 16 meters

Would you like further clarification or details?

Here are 5 related questions you can explore:

1. How do you solve quadratic equations using factorization?
2. What other methods can be used to find the roots of quadratic equations?
3. How do you calculate the perimeter of a rectangle with the given dimensions?
4. What is the formula for the diagonal of a rectangle, and how do you find it for this plot?
5. How would the equation change if the area of the plot were 600 m² instead of 528 m²?

Tip: When solving quadratic equations, always check for both the positive and negative roots to ensure the correct real-world interpretation.