A Carpet Is Laid On A Rectangle Floor Of Length 9 Meters And Breadth 6 Meters. This Leaves A Margin Of Width 1 Meter Round The Carpet. Find The Area Of The Carpet

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Introduction

In this problem, we are given a rectangle floor with a length of 9 meters and a breadth of 6 meters. A carpet is laid on this floor, leaving a margin of 1 meter around the carpet. Our goal is to find the area of the carpet. To do this, we need to understand the relationship between the dimensions of the floor, the margin, and the area of the carpet.

Understanding the Problem

Let's visualize the situation. The floor is a rectangle with a length of 9 meters and a breadth of 6 meters. The carpet is laid on this floor, leaving a margin of 1 meter around it. This means that the carpet is smaller than the floor, and the margin is the difference between the dimensions of the floor and the carpet.

Calculating the Dimensions of the Carpet

To find the area of the carpet, we need to know its dimensions. Let's call the length of the carpet "L" and the breadth of the carpet "B". Since the margin is 1 meter around the carpet, we can calculate the dimensions of the carpet as follows:

  • The length of the carpet (L) is equal to the length of the floor (9 meters) minus twice the margin (2 x 1 meter).
  • The breadth of the carpet (B) is equal to the breadth of the floor (6 meters) minus twice the margin (2 x 1 meter).

Using these formulas, we can calculate the dimensions of the carpet as follows:

  • L = 9 - 2 x 1 = 9 - 2 = 7 meters
  • B = 6 - 2 x 1 = 6 - 2 = 4 meters

Finding the Area of the Carpet

Now that we have the dimensions of the carpet, we can find its area. The area of a rectangle is given by the formula:

Area = Length x Breadth

Substituting the values we calculated earlier, we get:

Area = 7 x 4 = 28 square meters

Conclusion

In this problem, we found the area of a carpet laid on a rectangle floor with a length of 9 meters and a breadth of 6 meters, leaving a margin of 1 meter around the carpet. We calculated the dimensions of the carpet by subtracting twice the margin from the dimensions of the floor, and then found the area of the carpet using the formula for the area of a rectangle.

Mathematical Formulas Used

  • Length of the carpet (L) = Length of the floor - 2 x Margin
  • Breadth of the carpet (B) = Breadth of the floor - 2 x Margin
  • Area of the carpet = Length x Breadth

Real-World Applications

This problem has real-world applications in various fields, such as:

  • Interior Design: When designing a room, architects and interior designers need to calculate the area of the carpet to ensure it fits the space and meets the client's requirements.
  • Construction: Builders and contractors need to calculate the area of the carpet to determine the amount of materials needed for the project.
  • Furniture Arrangement: When arranging furniture in a room, it's essential to calculate the area of the carpet to ensure that the furniture fits comfortably and doesn't obstruct the space.

Tips and Variations

  • Variable Margin: In some cases, the margin around the carpet may vary. To account for this, we can modify the formulas to include the variable margin.
  • Non-Rectangular Floor: If the floor is not a rectangle, we need to use a different formula to calculate the area of the carpet.
  • Multiple Carpets: If there are multiple carpets in the room, we need to calculate the area of each carpet separately and then sum them up to find the total area.

Conclusion

Introduction

In our previous article, we discussed how to find the area of a carpet laid on a rectangle floor with a margin around it. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the formula to find the area of the carpet?

A: The formula to find the area of the carpet is:

Area = Length x Breadth

Where Length is the length of the carpet and Breadth is the breadth of the carpet.

Q: How do I calculate the dimensions of the carpet?

A: To calculate the dimensions of the carpet, you need to subtract twice the margin from the dimensions of the floor. The formula for the length of the carpet is:

L = Length of the floor - 2 x Margin

And the formula for the breadth of the carpet is:

B = Breadth of the floor - 2 x Margin

Q: What if the margin is not equal on all sides?

A: If the margin is not equal on all sides, you need to calculate the dimensions of the carpet separately for each side. For example, if the margin is 1 meter on the length and 2 meters on the breadth, you would calculate the length of the carpet as:

L = Length of the floor - 2 x Margin (length)

And the breadth of the carpet as:

B = Breadth of the floor - 2 x Margin (breadth)

Q: Can I use this formula for a non-rectangular floor?

A: No, this formula is only applicable for a rectangular floor. If the floor is not a rectangle, you need to use a different formula to calculate the area of the carpet.

Q: How do I calculate the area of multiple carpets?

A: To calculate the area of multiple carpets, you need to calculate the area of each carpet separately and then sum them up. For example, if you have two carpets with dimensions 3 meters x 4 meters and 5 meters x 6 meters, you would calculate the area of each carpet separately and then sum them up:

Area of carpet 1 = 3 x 4 = 12 square meters Area of carpet 2 = 5 x 6 = 30 square meters Total area = 12 + 30 = 42 square meters

Q: What if the carpet is not laid on a floor, but on a wall or a ceiling?

A: If the carpet is not laid on a floor, but on a wall or a ceiling, you need to use a different formula to calculate the area of the carpet. For example, if the carpet is laid on a wall with a length of 10 meters and a height of 5 meters, you would calculate the area of the carpet as:

Area = Length x Height = 10 x 5 = 50 square meters

Conclusion

In conclusion, finding the area of a carpet laid on a rectangle floor with a margin around it requires a clear understanding of the relationship between the dimensions of the floor, the margin, and the area of the carpet. By using mathematical formulas and real-world applications, we can ensure that the carpet fits the space and meets the client's requirements.

Frequently Asked Questions

  • Q: What is the formula to find the area of the carpet?
    • A: Area = Length x Breadth
  • Q: How do I calculate the dimensions of the carpet?
    • A: L = Length of the floor - 2 x Margin, B = Breadth of the floor - 2 x Margin
  • Q: What if the margin is not equal on all sides?
    • A: Calculate the dimensions of the carpet separately for each side
  • Q: Can I use this formula for a non-rectangular floor?
    • A: No, this formula is only applicable for a rectangular floor
  • Q: How do I calculate the area of multiple carpets?
    • A: Calculate the area of each carpet separately and then sum them up
  • Q: What if the carpet is not laid on a floor, but on a wall or a ceiling?
    • A: Use a different formula to calculate the area of the carpet