Calculating the Perimeter of a Rectangular Carpet in a Room

Understanding the dimensions and calculations of a rectangular carpet in a given room with a margin is a common geometry problem. This article will walk you through the process step-by-step, providing a clear solution and explanation, which is essential for those preparing for math exams or looking to improve their problem-solving skills.

Problem and Given Data

The problem we are dealing with is as follows: The floor of a room is 10 meters long and 8 meters wide. A rectangular carpet is placed at the center of the room, leaving a 3-meter margin all around. What is the perimeter of the carpet?

Let's break down the given data:

Total length of the room: 10 meters Total width of the room: 8 meters Marginal space around the carpet: 3 meters on each side

Solution Steps

We need to determine the dimensions of the carpet after accounting for the 3-meter margin on all sides.

Determining the Length of the Carpet

To find the length of the carpet, we subtract the margin on both sides:

Length of the carpet Total length of the room - 2 × Margin 10 meters - 2 × 3 meters 10 meters - 6 meters 4 meters

Determining the Width of the Carpet

Similarly, to find the width of the carpet, we subtract the margin on both sides:

Width of the carpet Total width of the room - 2 × Margin 8 meters - 2 × 3 meters 8 meters - 6 meters 2 meters

Calculating the Perimeter of the Carpet

The perimeter of a rectangle is given by the formula: Perimeter 2 × (Length Width) Substituting the values we've determined: Perimeter 2 × (4 meters 2 meters) 2 × 6 meters 12 meters

Visualizing the Problem

To better visualize the problem, imagine the room as a rectangle with a smaller rectangle (the carpet) placed within it, with a 3-meter border around the carpet.

Conclusion

The perimeter of the carpet, when a 3-meter margin is left all around, is 12 meters. This calculation is based on the basic principles of geometry and provides a clear example of how to solve real-world problems involving room dimensions and carpet placement.

Additional Information and Resources

For more problems and resources on geometry and other math topics, visit your local library, educational websites, and online learning platforms. Geometry is a fundamental skill that can be applied to various fields, from construction to design and planning.