The Perimeter and Area of a Rectangular Ground

Oct 13, 2025 by magicalceylontours.com 40 views

Introduction

In this article, we will explore the relationship between the perimeter and area of a rectangular ground. We will also delve into the roots of a quadratic equation and use this knowledge to find the length and breadth of the given ground. Additionally, we will discuss how many pieces of land can be made with the given ground.

The Perimeter and Area of a Rectangular Ground

The perimeter of a rectangle is given by the formula $2(l + b)$ , where $l$ is the length and $b$ is the breadth. The area of a rectangle is given by the formula $lb$ . In this problem, we are given that the perimeter of the rectangular ground is 66 m and the area is 260 sq. m.

Formula for Perimeter and Area

The formula for the perimeter of a rectangle is:

Perimeter = 2(l + b)

The formula for the area of a rectangle is:

Area = lb

Given Values

We are given that the perimeter of the rectangular ground is 66 m and the area is 260 sq. m.

Perimeter = 66 m Area = 260 sq. m

The Roots of a Quadratic Equation

A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. The general form of a quadratic equation is $ax^2 + bx + c = 0$ , where $a$ , $b$ , and $c$ are constants, and $a \neq 0$ . The roots of a quadratic equation are the values of $x$ that satisfy the equation.

Formula for Roots

The roots of a quadratic equation can be found using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Illustration of Roots

To illustrate the roots of a quadratic equation, let's consider the equation $x^2 + 4x + 4 = 0$ . We can factor this equation as $(x + 2)^2 = 0$ . This means that the only root of this equation is $x = -2$ .

Finding the Length and Breadth of the Given Ground

Now that we have discussed the perimeter and area of a rectangular ground and the roots of a quadratic equation, we can use this knowledge to find the length and breadth of the given ground.

Using the Perimeter Formula

We are given that the perimeter of the rectangular ground is 66 m. We can use the perimeter formula to write an equation:

2(l + b) = 66

Using the Area Formula

We are also given that the area of the rectangular ground is 260 sq. m. We can use the area formula to write another equation:

lb = 260

Solving the Equations

We can solve these two equations simultaneously to find the values of $l$ and $b$ .

2(l + b) = 66 lb = 260

Solution

Solving these equations, we get:

l = 20 m b = 13 m

How Many Pieces of Land Can Be Made with the Given Ground

Now that we have found the length and breadth of the given ground, we can use this knowledge to determine how many pieces of land can be made with the given ground.

Dividing the Ground

We can divide the ground into smaller pieces by drawing lines parallel to the length and breadth of the ground. Let's assume that we want to divide the ground into $n$ pieces.

Formula for Number of Pieces

The number of pieces of land that can be made with the given ground is given by the formula:

Number of Pieces = (l + b) / n

Substituting Values

We can substitute the values of $l$ and $b$ into this formula:

Number of Pieces = (20 + 13) / n Number of Pieces = 33 / n

Finding the Value of n

To find the value of $n$ , we need to know the total area of the ground. We are given that the area of the ground is 260 sq. m. We can use this information to find the value of $n$ .

Formula for Area

The area of the ground is given by the formula:

Area = lb 260 = 20 × 13

Finding the Value of n

We can rearrange this equation to solve for $n$ :

n = 260 / (20 × 13) n = 260 / 260 n = 1

Conclusion

In this article, we have discussed the perimeter and area of a rectangular ground, the roots of a quadratic equation, and how many pieces of land can be made with the given ground. We have used the perimeter and area formulas to find the length and breadth of the given ground, and we have used the quadratic formula to illustrate the roots of a quadratic equation. We have also used the formula for the number of pieces of land that can be made with the given ground to find the value of $n$ .

Introduction

In our previous article, we discussed the perimeter and area of a rectangular ground, the roots of a quadratic equation, and how many pieces of land can be made with the given ground. In this article, we will answer some frequently asked questions related to the perimeter and area of a rectangular ground.

Q&A

Q: What is the formula for the perimeter of a rectangle?

A: The formula for the perimeter of a rectangle is 2(l + b), where $l$ is the length and $b$ is the breadth.

Q: What is the formula for the area of a rectangle?

A: The formula for the area of a rectangle is lb, where $l$ is the length and $b$ is the breadth.

Q: How do I find the length and breadth of a rectangle if I know its perimeter and area?

A: To find the length and breadth of a rectangle, you can use the perimeter and area formulas. Let's say the perimeter is 66 m and the area is 260 sq. m. We can write two equations:

2(l + b) = 66 lb = 260

Solving these equations, we get:

l = 20 m b = 13 m

Q: What is the relationship between the perimeter and area of a rectangle?

A: The perimeter and area of a rectangle are related in that the perimeter is the distance around the rectangle, while the area is the amount of space inside the rectangle.

Q: How do I find the number of pieces of land that can be made with a given ground?

A: To find the number of pieces of land that can be made with a given ground, you can use the formula:

Number of Pieces = (l + b) / n

where $l$ and $b$ are the length and breadth of the ground, and $n$ is the number of pieces you want to divide the ground into.

Q: What is the formula for the roots of a quadratic equation?

A: The formula for the roots of a quadratic equation is:

x = (-b ± √(b^2 - 4ac)) / 2a

where $a$ , $b$ , and $c$ are the coefficients of the quadratic equation.

Q: How do I illustrate the roots of a quadratic equation?

A: To illustrate the roots of a quadratic equation, you can factor the equation or use the quadratic formula to find the roots.

Q: What is the significance of the quadratic formula?

A: The quadratic formula is a powerful tool for finding the roots of a quadratic equation. It can be used to solve a wide range of problems in mathematics and science.

Conclusion

In this article, we have answered some frequently asked questions related to the perimeter and area of a rectangular ground. We have discussed the formulas for the perimeter and area of a rectangle, the relationship between the perimeter and area, and how to find the number of pieces of land that can be made with a given ground. We have also discussed the quadratic formula and how to illustrate the roots of a quadratic equation.

Additional Resources

For more information on the perimeter and area of a rectangle, see our previous article: "The Perimeter and Area of a Rectangular Ground".
For more information on the quadratic formula, see our article: "The Quadratic Formula: A Powerful Tool for Solving Quadratic Equations".
For more information on mathematics and science, see our website: "Mathematics and Science: A Comprehensive Resource".