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

To find the length and breadth of the rectangular plot, we can set up some equations based on the information given.

Defining Variables

Let the breadth of the plot be represented as b. According to the problem, the length l can be expressed as:

• l = 2b + 1

Setting Up the Area Equation

The area of a rectangle is calculated by multiplying its length and breadth. Given that the area is 528 m², we can write:

• l × b = 528

Substituting the expression for length into the area equation gives:

• (2b + 1) × b = 528

Solving the Equation

Expanding this equation results in:

• 2b² + b - 528 = 0

This is a quadratic equation in the standard form ax² + bx + c = 0, where:

• a = 2
• b = 1
• c = -528

Using the Quadratic Formula

We can apply the quadratic formula:

• b = [-B ± √(B² - 4AC)] / 2A

Substituting the values:

• b = [-1 ± √(1² - 4 × 2 × -528)] / (2 × 2)

This simplifies to:

• b = [-1 ± √(1 + 4224)] / 4

Calculating further:

• b = [-1 ± √4225] / 4

Since √4225 = 65, we have:

• b = [-1 + 65] / 4 = 64 / 4 = 16

Finding the Length

Now that we have the breadth, we can find the length:

• l = 2b + 1 = 2(16) + 1 = 32 + 1 = 33

Final Dimensions

The dimensions of the rectangular plot are:

• Breadth: 16 m
• Length: 33 m