A Carpet In Frank's House Has A Length Of 2 1 4 2 \frac{1}{4} 2 4 1 ​ Meters And A Width Of 1 1 5 1 \frac{1}{5} 1 5 1 ​ Meters. What Is The Perimeter Of The Carpet?A. 9 10 \frac{9}{10} 10 9 ​ Meters B. 3 9 20 3 \frac{9}{20} 3 20 9 ​ Meters C. $2

Introduction

In this article, we will delve into the world of mathematics and explore the concept of calculating the perimeter of a carpet. The perimeter of a shape is the total length of its boundary, and it is an essential concept in geometry. We will use a real-life example to demonstrate how to calculate the perimeter of a carpet with a given length and width.

Understanding the Problem

The problem states that a carpet in Frank's house has a length of $2 \frac{1}{4}$ meters and a width of $1 \frac{1}{5}$ meters. To calculate the perimeter of the carpet, we need to add the lengths of all its sides. Since the carpet is a rectangle, we have two pairs of equal sides.

Converting Mixed Numbers to Improper Fractions

Before we can calculate the perimeter, we need to convert the mixed numbers to improper fractions. To do this, we multiply the whole number part by the denominator and add the numerator.

• $2 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}$
• $1 \frac{1}{5} = \frac{(1 \times 5) + 1}{5} = \frac{5 + 1}{5} = \frac{6}{5}$

Calculating the Perimeter

Now that we have the length and width in improper fractions, we can calculate the perimeter. The perimeter of a rectangle is given by the formula:

$P = 2l + 2w$

where $l$ is the length and $w$ is the width.

Substituting the values, we get:

$P = 2\left(\frac{9}{4}\right) + 2\left(\frac{6}{5}\right)$

To add these fractions, we need to find a common denominator, which is 20.

$P = \frac{2 \times 9 \times 5}{4 \times 5} + \frac{2 \times 6 \times 4}{5 \times 4}$ $P = \frac{90}{20} + \frac{48}{20}$ $P = \frac{90 + 48}{20}$ $P = \frac{138}{20}$

Simplifying the Fraction

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

$P = \frac{138 \div 2}{20 \div 2}$ $P = \frac{69}{10}$

Conclusion

In conclusion, the perimeter of the carpet is $\frac{69}{10}$ meters. This is the final answer to the problem.

Discussion

The perimeter of a shape is an essential concept in geometry, and it has many real-life applications. In this article, we used a real-life example to demonstrate how to calculate the perimeter of a carpet with a given length and width. We also converted mixed numbers to improper fractions and simplified the fraction to get the final answer.

Common Mistakes

When calculating the perimeter of a shape, it is essential to remember that the perimeter is the total length of its boundary. It is not the same as the area of the shape. Also, when adding fractions, it is essential to find a common denominator to get the correct answer.

Real-Life Applications

The concept of perimeter has many real-life applications. For example, when building a fence around a garden or a house, we need to calculate the perimeter of the shape to determine the length of the fence required. Similarly, when designing a room or a building, we need to calculate the perimeter of the shape to determine the length of the walls required.

Final Answer

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Introduction

In our previous article, we explored the concept of calculating the perimeter of a carpet with a given length and width. We used a real-life example to demonstrate how to calculate the perimeter of a carpet with a length of $2 \frac{1}{4}$ meters and a width of $1 \frac{1}{5}$ meters. In this article, we will provide a Q&A guide to help you understand the concept of perimeter and how to calculate it.

Q: What is the perimeter of a shape?

A: The perimeter of a shape is the total length of its boundary. It is an essential concept in geometry and has many real-life applications.

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

A: To calculate the perimeter of a rectangle, you need to add the lengths of all its sides. The formula for the perimeter of a rectangle is:

$P = 2l + 2w$

where $l$ is the length and $w$ is the width.

Q: What if the length and width are given as mixed numbers?

A: If the length and width are given as mixed numbers, you need to convert them to improper fractions before calculating the perimeter. To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator and add the numerator.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators.

Q: What is the perimeter of the carpet in Frank's house?

A: The perimeter of the carpet in Frank's house is $\frac{69}{10}$ meters.

Q: Can I use a calculator to calculate the perimeter?

A: Yes, you can use a calculator to calculate the perimeter. However, it is essential to understand the concept of perimeter and how to calculate it manually.

Q: What are some real-life applications of the concept of perimeter?

A: The concept of perimeter has many real-life applications, such as:

• Building a fence around a garden or a house
• Designing a room or a building
• Calculating the length of a border or a border strip

Q: What are some common mistakes to avoid when calculating the perimeter?

A: Some common mistakes to avoid when calculating the perimeter include:

• Confusing the perimeter with the area of the shape
• Not finding a common denominator when adding fractions
• Not converting mixed numbers to improper fractions

Conclusion

In conclusion, the concept of perimeter is an essential concept in geometry, and it has many real-life applications. We hope this Q&A guide has helped you understand the concept of perimeter and how to calculate it.

Final Answer

The final answer to the problem is $\boxed{\frac{69}{10}}$ meters.

Additional Resources

If you want to learn more about the concept of perimeter, we recommend the following resources:

• Khan Academy: Perimeter and Area
• Math Open Reference: Perimeter of a Rectangle
• IXL: Perimeter and Area

We hope this Q&A guide has been helpful in understanding the concept of perimeter. If you have any further questions, please don't hesitate to ask.