The Length And Breadth Of A Rectangular Piece Of Land Are In The Ratio 5 : 2 Find The Cost Of Plotting It At The Rate Of ₹25 Per M.sq And Perimeter Is 120 M
Introduction
In this article, we will delve into the world of mathematics to explore the length and breadth of a rectangular piece of land. We will use the given ratio of 5:2 to find the dimensions of the land and then calculate the cost of plotting it at the rate of ₹25 per m². Additionally, we will use the given perimeter to verify our calculations.
Understanding the Ratio
The ratio of the length to the breadth of the rectangular piece of land is given as 5:2. This means that for every 5 units of length, the breadth is 2 units. We can represent this ratio as a fraction, where the length is 5x and the breadth is 2x.
Finding the Dimensions
We are given that the perimeter of the rectangular piece of land is 120 meters. The formula for the perimeter of a rectangle is 2(length + breadth). We can use this formula to set up an equation and solve for the value of x.
2(5x + 2x) = 120
Combine like terms:
2(7x) = 120
Multiply both sides by 2:
14x = 120
Divide both sides by 14:
x = 120/14
x = 8.57 (approximately)
Now that we have the value of x, we can find the length and breadth of the rectangular piece of land.
Length = 5x = 5(8.57) = 42.85 meters (approximately)
Breadth = 2x = 2(8.57) = 17.14 meters (approximately)
Calculating the Area
The area of a rectangle is given by the formula length × breadth. We can use this formula to calculate the area of the rectangular piece of land.
Area = length × breadth = 42.85 × 17.14 = 733.19 m² (approximately)
Calculating the Cost of Plotting
The cost of plotting the rectangular piece of land is given at the rate of ₹25 per m². We can use this rate to calculate the total cost of plotting the land.
Total Cost = Area × Rate = 733.19 × 25 = ₹18,329.75 (approximately)
Conclusion
In this article, we used the given ratio of 5:2 to find the dimensions of a rectangular piece of land. We then calculated the area of the land and used the given rate to find the cost of plotting it. The perimeter of the land was also used to verify our calculations. We hope that this article has provided a clear understanding of the mathematical concepts involved in finding the length and breadth of a rectangular piece of land.
Mathematical Formulas Used
- Perimeter of a rectangle: 2(length + breadth)
- Area of a rectangle: length × breadth
Real-World Applications
The concepts of length, breadth, and area are essential in various real-world applications, such as:
- Architecture: to design buildings and structures
- Engineering: to calculate the dimensions of machines and equipment
- Geography: to measure the size of countries and territories
- Business: to calculate the cost of land and property
Limitations of the Article
This article assumes that the reader has a basic understanding of mathematical concepts, such as ratios and formulas. Additionally, the article uses approximate values for the dimensions and area of the rectangular piece of land. In a real-world scenario, the dimensions and area would be calculated with greater precision.
Future Research Directions
Future research could involve exploring the mathematical concepts involved in finding the length and breadth of a rectangular piece of land in more complex scenarios, such as:
- Using different shapes and sizes of land
- Incorporating obstacles and irregularities in the land
- Calculating the cost of plotting the land in different currencies and exchange rates
Frequently Asked Questions (FAQs) on the Length and Breadth of a Rectangular Piece of Land =====================================================================================
Q: What is the ratio of the length to the breadth of the rectangular piece of land?
A: The ratio of the length to the breadth of the rectangular piece of land is given as 5:2.
Q: How do I find the dimensions of the rectangular piece of land using the given ratio?
A: To find the dimensions of the rectangular piece of land, you can use the given ratio to set up an equation. Let the length be 5x and the breadth be 2x. Then, use the formula for the perimeter of a rectangle to set up an equation and solve for the value of x.
Q: What is the formula for the perimeter of a rectangle?
A: The formula for the perimeter of a rectangle is 2(length + breadth).
Q: How do I calculate the area of the rectangular piece of land?
A: To calculate the area of the rectangular piece of land, you can use the formula length × breadth.
Q: What is the cost of plotting the rectangular piece of land at the rate of ₹25 per m²?
A: To calculate the cost of plotting the rectangular piece of land, you can multiply the area of the land by the given rate.
Q: Can I use different shapes and sizes of land to calculate the cost of plotting?
A: Yes, you can use different shapes and sizes of land to calculate the cost of plotting. However, you will need to use different formulas and calculations to find the area and perimeter of the land.
Q: How do I incorporate obstacles and irregularities in the land when calculating the cost of plotting?
A: To incorporate obstacles and irregularities in the land when calculating the cost of plotting, you will need to use more complex formulas and calculations. This may involve using trigonometry and geometry to find the area and perimeter of the land.
Q: Can I calculate the cost of plotting the land in different currencies and exchange rates?
A: Yes, you can calculate the cost of plotting the land in different currencies and exchange rates. However, you will need to use different exchange rates and conversion formulas to find the equivalent cost in the desired currency.
Q: What are some real-world applications of the concepts of length, breadth, and area?
A: Some real-world applications of the concepts of length, breadth, and area include:
- Architecture: to design buildings and structures
- Engineering: to calculate the dimensions of machines and equipment
- Geography: to measure the size of countries and territories
- Business: to calculate the cost of land and property
Q: What are some limitations of this article?
A: Some limitations of this article include:
- Assuming a basic understanding of mathematical concepts
- Using approximate values for the dimensions and area of the rectangular piece of land
- Not incorporating obstacles and irregularities in the land
Q: What are some future research directions for this topic?
A: Some future research directions for this topic include:
- Exploring the mathematical concepts involved in finding the length and breadth of a rectangular piece of land in more complex scenarios
- Incorporating obstacles and irregularities in the land
- Calculating the cost of plotting the land in different currencies and exchange rates
Q: How can I apply the concepts of length, breadth, and area in my daily life?
A: You can apply the concepts of length, breadth, and area in your daily life by using them to calculate the dimensions and area of objects and spaces. This can be useful in a variety of situations, such as:
- Measuring the size of a room or a piece of furniture
- Calculating the cost of materials for a project
- Designing a layout for a room or a space