The area of a rectangular plot is 528
m
2
.
 The length of the plot (in metres) is one than twice its breadth. We need to find the length and breadth of the plot.

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.

The area of a rectangular plot is 528 m². The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot.

Find the length and breadth of a rectangular plot with an area of 528 m². This problem uses algebraic methods and quadratic equations to solve for dimensions, making it perfect for students in Grades 8-10.

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