Understanding the Relationship Between Length and Breadth

Oct 13, 2025 by talynt.org 126 views

Introduction

In this problem, we are given a rectangular land with a specific relationship between its length and breadth. We are also given the area of the land, which is 648 m². Our goal is to find the length, breadth, and perimeter of the land.

Understanding the Relationship Between Length and Breadth

Let's assume that the breadth of the land is represented by the variable 'b'. Since the length of the land is twice the breadth, we can represent the length as 2b.

Calculating the Area of the Land

The area of a rectangle is given by the formula: Area = Length × Breadth. In this case, the area is 648 m², and the length is 2b. So, we can write the equation as:

648 = 2b × b

Simplifying the Equation

We can simplify the equation by multiplying the terms on the right-hand side:

648 = 2b²

Dividing Both Sides by 2

To isolate the term b², we can divide both sides of the equation by 2:

324 = b²

Taking the Square Root of Both Sides

To find the value of b, we can take the square root of both sides of the equation:

b = √324

Evaluating the Square Root

The square root of 324 is 18. So, we can write:

b = 18

Finding the Length of the Land

Since the length of the land is twice the breadth, we can find the length by multiplying the breadth by 2:

Length = 2b = 2 × 18 = 36

Calculating the Perimeter of the Land

The perimeter of a rectangle is given by the formula: Perimeter = 2(Length + Breadth). In this case, the length is 36, and the breadth is 18. So, we can write the equation as:

Perimeter = 2(36 + 18) = 2 × 54 = 108

Conclusion

In this problem, we were given a rectangular land with a specific relationship between its length and breadth. We were also given the area of the land, which is 648 m². By using the formula for the area of a rectangle and simplifying the equation, we were able to find the length, breadth, and perimeter of the land. The length of the land is 36 m, the breadth is 18 m, and the perimeter is 108 m.

Key Takeaways

The length of the land is twice the breadth.
The area of the land is 648 m².
The perimeter of the land is 108 m.

Real-World Applications

This problem has real-world applications in various fields such as architecture, engineering, and urban planning. For example, when designing a building or a park, architects and engineers need to consider the dimensions of the land and the perimeter of the building or park.

Future Research Directions

This problem can be extended to more complex scenarios, such as finding the dimensions of a rectangular land with a specific perimeter or area. Additionally, researchers can explore the application of this problem in other fields such as computer science and data analysis.

References

[1] Khan Academy. (n.d.). Area of a rectangle. Retrieved from https://www.khanacademy.org/math/geometry/geometry-of-rectangles/area-of-a-rectangle/v/area-of-a-rectangle
[2] Math Open Reference. (n.d.). Perimeter of a rectangle. Retrieved from https://www.mathopenref.com/rectangleperimeter.html

Glossary

Breadth: The width of a rectangle.
Length: The distance between two opposite sides of a rectangle.
Perimeter: The distance around a rectangle.
Rectangle: A four-sided shape with opposite sides of equal length.

FAQs

Q: What is the length of the land? A: The length of the land is 36 m.
Q: What is the breadth of the land? A: The breadth of the land is 18 m.
Q: What is the perimeter of the land? A: The perimeter of the land is 108 m.

Introduction

In our previous article, we discussed the problem of finding the length, breadth, and perimeter of a rectangular land with a specific relationship between its length and breadth. In this article, we will answer some frequently asked questions (FAQs) related to this topic.

Q&A

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

A: The formula for the area of a rectangle is: Area = Length × Breadth.

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

A: To find the length of a rectangle, you can use the formula: Length = Area ÷ Breadth.

Q: What is the relationship between the length and breadth of a rectangle?

A: The length of a rectangle is typically twice the breadth, but this can vary depending on the specific problem.

Q: How do I find the perimeter of a rectangle?

A: To find the perimeter of a rectangle, you can use the formula: Perimeter = 2(Length + Breadth).

Q: What is the difference between the length and breadth of a rectangle?

A: The length of a rectangle is the distance between two opposite sides, while the breadth is the width of the rectangle.

Q: Can I use the same formula to find the area of a square?

A: Yes, you can use the same formula to find the area of a square, but you will need to know the length of one side of the square.

Q: How do I find the length of a square if I know its area?

A: To find the length of a square, you can use the formula: Length = √Area.

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

A: The area of a rectangle is equal to the product of its length and breadth, while the perimeter is equal to the sum of its four sides.

Q: Can I use the same formula to find the perimeter of a square?

A: Yes, you can use the same formula to find the perimeter of a square, but you will need to know the length of one side of the square.

Q: How do I find the perimeter of a square?

A: To find the perimeter of a square, you can use the formula: Perimeter = 4 × Length.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) related to rectangular lands. We hope that this information will be helpful to you in understanding the concepts of length, breadth, and perimeter of a rectangle.

Key Takeaways

The formula for the area of a rectangle is: Area = Length × Breadth.
The formula for the length of a rectangle is: Length = Area ÷ Breadth.
The formula for the perimeter of a rectangle is: Perimeter = 2(Length + Breadth).
The length of a rectangle is typically twice the breadth.
The perimeter of a rectangle is equal to the sum of its four sides.

Real-World Applications

This information has real-world applications in various fields such as architecture, engineering, and urban planning. For example, when designing a building or a park, architects and engineers need to consider the dimensions of the land and the perimeter of the building or park.

Future Research Directions

This topic can be extended to more complex scenarios, such as finding the dimensions of a rectangular land with a specific perimeter or area. Additionally, researchers can explore the application of this topic in other fields such as computer science and data analysis.

References

[1] Khan Academy. (n.d.). Area of a rectangle. Retrieved from https://www.khanacademy.org/math/geometry/geometry-of-rectangles/area-of-a-rectangle/v/area-of-a-rectangle
[2] Math Open Reference. (n.d.). Perimeter of a rectangle. Retrieved from https://www.mathopenref.com/rectangleperimeter.html

Glossary

Breadth: The width of a rectangle.
Length: The distance between two opposite sides of a rectangle.
Perimeter: The distance around a rectangle.
Rectangle: A four-sided shape with opposite sides of equal length.
Square: A four-sided shape with all sides of equal length.

FAQs

Q: What is the formula for the area of a rectangle? A: The formula for the area of a rectangle is: Area = Length × Breadth.
Q: How do I find the length of a rectangle if I know its area and breadth? A: To find the length of a rectangle, you can use the formula: Length = Area ÷ Breadth.
Q: What is the relationship between the length and breadth of a rectangle? A: The length of a rectangle is typically twice the breadth, but this can vary depending on the specific problem.
Q: How do I find the perimeter of a rectangle? A: To find the perimeter of a rectangle, you can use the formula: Perimeter = 2(Length + Breadth).