Calculating the Perimeter of the Rug

Oct 13, 2025 by wbrum.org 149 views

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Introduction

In this article, we will explore the concept of calculating the width of a border around a rug. We will use a real-life scenario to demonstrate how to apply mathematical concepts to solve a problem. Our goal is to find the width of the border that Sabrina will place around her rug.

Understanding the Problem

Sabrina has a rug with a perimeter of 18 feet. The length of the rug is 8 feet, and the width is 4 feet. To find the width of the border, we need to first calculate the total area of the rug and then add the area of the border. However, we are not given the area of the border, so we will need to use the perimeter of the rug to find the width of the border.

Calculating the Perimeter of the Rug

The perimeter of a rectangle is given by the formula:

P = 2(l + w)

where P is the perimeter, l is the length, and w is the width.

In this case, the perimeter of the rug is 18 feet, the length is 8 feet, and the width is 4 feet. We can plug these values into the formula to get:

18 = 2(8 + 4)

Solving for the Width of the Border

To find the width of the border, we need to first find the total area of the rug. The area of a rectangle is given by the formula:

A = l × w

where A is the area, l is the length, and w is the width.

In this case, the area of the rug is:

A = 8 × 4 = 32 square feet

Now, we need to find the area of the border. Since the perimeter of the rug is 18 feet, we can set up an equation to represent the total area of the rug and the border:

A + (border area) = 18 × (length + width)

We know that the area of the rug is 32 square feet, so we can plug this value into the equation:

32 + (border area) = 18 × (8 + 4)

Simplifying the Equation

To simplify the equation, we can first calculate the total length and width of the rug and the border:

8 + 4 = 12 feet

Now, we can plug this value into the equation:

32 + (border area) = 18 × 12

Solving for the Border Area

To solve for the border area, we can first calculate the total area of the rug and the border:

18 × 12 = 216 square feet

Now, we can subtract the area of the rug from the total area to find the border area:

border area = 216 - 32 = 184 square feet

Finding the Width of the Border

Now that we have found the border area, we can use the formula for the area of a rectangle to find the width of the border:

A = l × w

where A is the area, l is the length, and w is the width.

In this case, the area of the border is 184 square feet, and the length is 12 feet (the total length of the rug and the border). We can plug these values into the formula to get:

184 = 12 × w

Solving for the Width of the Border

To solve for the width of the border, we can divide both sides of the equation by 12:

w = 184 ÷ 12 = 15.33 feet

Conclusion

In this article, we used a real-life scenario to demonstrate how to calculate the width of a border around a rug. We first calculated the perimeter of the rug and then used the formula for the area of a rectangle to find the width of the border. Our final answer is that the width of the border is approximately 15.33 feet.

Mathematical Formulas Used

Perimeter of a rectangle: P = 2(l + w)
Area of a rectangle: A = l × w

Real-Life Applications

This problem can be applied to real-life scenarios such as:

Calculating the width of a border around a room
Finding the width of a border around a piece of furniture
Determining the width of a border around a garden or a lawn

Tips and Tricks

When calculating the perimeter of a rectangle, make sure to add the length and width together.
When calculating the area of a rectangle, make sure to multiply the length and width together.
When solving for the width of a border, make sure to divide both sides of the equation by the length.

Practice Problems

A rug has a perimeter of 20 feet. The length of the rug is 6 feet, and the width is 3 feet. What is the width of the border?
A room has a perimeter of 30 feet. The length of the room is 10 feet, and the width is 5 feet. What is the width of the border?
A garden has a perimeter of 40 feet. The length of the garden is 12 feet, and the width is 6 feet. What is the width of the border?

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Q: What is the formula for calculating the width of a border?

A: The formula for calculating the width of a border is:

P = 2(l + w)

where P is the perimeter, l is the length, and w is the width.

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

A: To calculate the perimeter of a rectangle, you need to add the length and width together and multiply by 2:

P = 2(l + w)

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

A: The perimeter of a rectangle is the distance around the outside of the rectangle, while the area of a rectangle is the amount of space inside the rectangle.

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

A: To calculate the area of a rectangle, you need to multiply the length and width together:

A = l × w

Q: Can I use the same formula to calculate the width of a border for a square?

A: Yes, you can use the same formula to calculate the width of a border for a square. However, you need to make sure that the length and width are the same.

Q: What if I don't know the length or width of the rectangle?

A: If you don't know the length or width of the rectangle, you can use the formula for the perimeter to find the missing value.

Q: Can I use a calculator to calculate the width of a border?

A: Yes, you can use a calculator to calculate the width of a border. However, make sure to enter the correct values and follow the correct order of operations.

Q: What if I make a mistake when calculating the width of a border?

A: If you make a mistake when calculating the width of a border, you can try rechecking your work or using a different method to calculate the answer.

Q: Can I use the formula for the width of a border to calculate the width of a border for a circle?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a circle. The formula for the width of a border is only applicable to rectangles and squares.

Q: What is the significance of the width of a border in real-life applications?

A: The width of a border is significant in real-life applications such as:

Calculating the width of a border around a room
Finding the width of a border around a piece of furniture
Determining the width of a border around a garden or a lawn

Q: Can I use the formula for the width of a border to calculate the width of a border for a 3D shape?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a 3D shape. The formula for the width of a border is only applicable to 2D shapes such as rectangles and squares.

Q: What if I need to calculate the width of a border for a shape with an irregular perimeter?

A: If you need to calculate the width of a border for a shape with an irregular perimeter, you may need to use a different method such as graphing or using a computer program.

Q: Can I use the formula for the width of a border to calculate the width of a border for a shape with a curved edge?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a shape with a curved edge. The formula for the width of a border is only applicable to shapes with straight edges.

Q: What if I need to calculate the width of a border for a shape with multiple sides?

A: If you need to calculate the width of a border for a shape with multiple sides, you may need to use a different method such as graphing or using a computer program.

Q: Can I use the formula for the width of a border to calculate the width of a border for a shape with a non-rectangular base?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a shape with a non-rectangular base. The formula for the width of a border is only applicable to shapes with rectangular bases.

Q: What if I need to calculate the width of a border for a shape with a variable perimeter?

A: If you need to calculate the width of a border for a shape with a variable perimeter, you may need to use a different method such as graphing or using a computer program.

Q: Can I use the formula for the width of a border to calculate the width of a border for a shape with a non-constant width?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a shape with a non-constant width. The formula for the width of a border is only applicable to shapes with constant widths.

Q: What if I need to calculate the width of a border for a shape with a complex perimeter?

A: If you need to calculate the width of a border for a shape with a complex perimeter, you may need to use a different method such as graphing or using a computer program.

Q: Can I use the formula for the width of a border to calculate the width of a border for a shape with a non-rectangular perimeter?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a shape with a non-rectangular perimeter. The formula for the width of a border is only applicable to shapes with rectangular perimeters.

Q: What if I need to calculate the width of a border for a shape with a variable length?

A: If you need to calculate the width of a border for a shape with a variable length, you may need to use a different method such as graphing or using a computer program.

Q: Can I use the formula for the width of a border to calculate the width of a border for a shape with a non-constant length?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a shape with a non-constant length. The formula for the width of a border is only applicable to shapes with constant lengths.

Q: What if I need to calculate the width of a border for a shape with a complex length?

A: If you need to calculate the width of a border for a shape with a complex length, you may need to use a different method such as graphing or using a computer program.

Q: Can I use the formula for the width of a border to calculate the width of a border for a shape with a non-rectangular length?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a shape with a non-rectangular length. The formula for the width of a border is only applicable to shapes with rectangular lengths.

Q: What if I need to calculate the width of a border for a shape with a variable width?

A: If you need to calculate the width of a border for a shape with a variable width, you may need to use a different method such as graphing or using a computer program.

Q: Can I use the formula for the width of a border to calculate the width of a border for a shape with a non-constant width?

Q: What if I need to calculate the width of a border for a shape with a complex width?

A: If you need to calculate the width of a border for a shape with a complex width, you may need to use a different method such as graphing or using a computer program.

Q: Can I use the formula for the width of a border to calculate the width of a border for a shape with a non-rectangular width?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a shape with a non-rectangular width. The formula for the width of a border is only applicable to shapes with rectangular widths.

Q: What if I need to calculate the width of a border for a shape with a variable perimeter and length?

A: If you need to calculate the width of a border for a shape with a variable perimeter and length, you may need to use a different method such as graphing or using a computer program.

Q: Can I use the formula for the width of a border to calculate the width of a border for a shape with a non-constant perimeter and length?

A: No, you cannot use the formula for the width of a border to calculate the width of a border for a shape with a non-constant perimeter and length. The formula for the width of a border is only applicable to shapes with constant perimeters and lengths.