Which Expression Correctly Represents The Perimeter Of A Rectangle That Is 12 Centimeters Long And 7 Centimeters Wide?A) $12 \, \text{cm} + 7 \, \text{cm}$B) $2(12 \, \text{cm}) + 7 \, \text{cm}$C) $12 \, \text{cm} + 2(7 \,

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Introduction

In geometry, the perimeter of a rectangle is the total length of its boundary. It is an essential concept in mathematics, and understanding how to calculate it is crucial for solving various problems. In this article, we will explore the correct expression for the perimeter of a rectangle that is 12 centimeters long and 7 centimeters wide.

What is the Perimeter of a Rectangle?

The perimeter of a rectangle is calculated by adding the lengths of all its sides. Since a rectangle has two pairs of equal sides, we can calculate the perimeter by adding the lengths of two adjacent sides and then multiplying the result by 2.

Calculating the Perimeter

Let's consider a rectangle with a length of 12 centimeters and a width of 7 centimeters. To calculate the perimeter, we need to add the lengths of two adjacent sides and then multiply the result by 2.

The correct expression for the perimeter of a rectangle is:

2(l + w)

where l is the length and w is the width.

Evaluating the Options

Now, let's evaluate the given options to determine which one correctly represents the perimeter of the rectangle.

Option A: 12 cm+7 cm12 \, \text{cm} + 7 \, \text{cm}

This option is incorrect because it only adds the lengths of two adjacent sides without multiplying the result by 2.

Option B: 2(12 cm)+7 cm2(12 \, \text{cm}) + 7 \, \text{cm}

This option is also incorrect because it multiplies the length by 2 and then adds the width, which is not the correct order.

Option C: 12 cm+2(7 cm)12 \, \text{cm} + 2(7 \, \text{cm})

This option is correct because it adds the length and twice the width, which is the correct expression for the perimeter of a rectangle.

Conclusion

In conclusion, the correct expression for the perimeter of a rectangle that is 12 centimeters long and 7 centimeters wide is:

12 cm + 2(7 cm)

This expression correctly represents the perimeter of the rectangle by adding the length and twice the width.

Why is this Important?

Understanding the perimeter of a rectangle is crucial in various mathematical applications, such as:

  • Calculating the area of a rectangle
  • Finding the perimeter of a rectangle with different dimensions
  • Solving problems involving rectangles in real-world scenarios

Real-World Applications

The concept of the perimeter of a rectangle has numerous real-world applications, such as:

  • Architecture: Calculating the perimeter of a building to determine the amount of materials needed for construction.
  • Engineering: Designing rectangular structures, such as bridges or tunnels, by calculating their perimeter.
  • Art: Creating rectangular shapes in art, such as paintings or sculptures, by understanding the perimeter of the shape.

Tips and Tricks

Here are some tips and tricks to help you understand the perimeter of a rectangle:

  • Always remember that the perimeter of a rectangle is calculated by adding the lengths of two adjacent sides and then multiplying the result by 2.
  • Use the correct expression for the perimeter, which is 2(l + w).
  • Practice calculating the perimeter of rectangles with different dimensions to become more comfortable with the concept.

Conclusion

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions about the perimeter of a rectangle.

Q: What is the perimeter of a rectangle?

A: The perimeter of a rectangle is the total length of its boundary. It is calculated by adding the lengths of all its sides.

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 two adjacent sides and then multiply the result by 2. The correct expression for the perimeter is 2(l + w), where l is the length and w is the width.

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

A: The perimeter of a rectangle is the total length of its boundary, while the area of a rectangle is the amount of space inside the rectangle. The perimeter is calculated by adding the lengths of all its sides, while the area is calculated by multiplying the length and width.

Q: Can I use a formula to calculate the perimeter of a rectangle?

A: Yes, you can use the formula 2(l + w) to calculate the perimeter of a rectangle. This formula is a simplified way of calculating the perimeter by adding the lengths of two adjacent sides and then multiplying the result by 2.

Q: What if I have a rectangle with different dimensions? How do I calculate the perimeter?

A: To calculate the perimeter of a rectangle with different dimensions, you can use the same formula 2(l + w). Simply substitute the length and width of the rectangle into the formula and calculate the result.

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

A: Yes, you can use a calculator to calculate the perimeter of a rectangle. Simply enter the length and width of the rectangle into the calculator and use the formula 2(l + w) to calculate the result.

Q: What are some real-world applications of the perimeter of a rectangle?

A: The perimeter of a rectangle has numerous real-world applications, such as:

  • Architecture: Calculating the perimeter of a building to determine the amount of materials needed for construction.
  • Engineering: Designing rectangular structures, such as bridges or tunnels, by calculating their perimeter.
  • Art: Creating rectangular shapes in art, such as paintings or sculptures, by understanding the perimeter of the shape.

Q: How can I practice calculating the perimeter of a rectangle?

A: You can practice calculating the perimeter of a rectangle by using online calculators or worksheets. You can also try calculating the perimeter of rectangles with different dimensions to become more comfortable with the concept.

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

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

  • Forgetting to multiply the result by 2
  • Adding the lengths of two adjacent sides without multiplying the result by 2
  • Using the wrong formula or expression for the perimeter

Conclusion

In conclusion, the perimeter of a rectangle is an essential concept in mathematics that has numerous real-world applications. By understanding how to calculate the perimeter of a rectangle, you can become more confident in your ability to solve various problems and make informed decisions in various fields.