Recarpeting a Rectangular Room: A Comprehensive Guide to Calculating Cost and Dimensions

When it comes to enhancing the aesthetics and comfort of your home, recarpeting a rectangular room can make a significant difference. Understanding the size of your room is essential when it comes to purchasing the right amount of carpet. In this article, we will guide you through the process of calculating the dimensions of a rectangular room based on its cost and the price per square foot of the carpet. Let's dive into how to solve such a problem step-by-step.

Understanding the Problem

You have a rectangular room that you want to recarpet. The carpet sells for $5 per square foot, and the total cost to recarpet the room is $1260. Your goal is to find out the dimensions of the room, specifically the width, given that the length of the room is 18 feet.

Calculating the Area of the Room

First, let's recall the basic formula for the area of a rectangle, which is Area Length × Width or lw.

Given:

The cost to recarpet the room is $1260. The cost per square foot of the carpet is $5. The length of the rectangular room is 18 feet.

To find the area of the carpet, we use the following formula:

Area Total Cost / Cost per Square Foot

Plugging in the given values:

Area 1260 / 5

Area 252 square feet

So, the area of the room is 252 square feet.

Finding the Width of the Room

Now that we know the area of the room, we can use the area formula to find the width. Let's denote the width of the room as W.

Recall the area formula for a rectangle:

Area Length × Width

Substitute the known values:

252 18 × W

To solve for W, divide both sides of the equation by 18:

W 252 / 18

W 14 feet

Therefore, the width of the room is 14 feet.

Conclusion

Recarpeting can transform your living space, and knowing the dimensions of your room is crucial. By understanding how to calculate the area and dimensions of a rectangular room, you can make informed decisions when it comes to carpeting and other home improvement projects. The width of your room, as calculated, is 14 feet, which can help in selecting the right amount of carpet and other furnishings to fit your space.

Now that you understand the process, here are a few tips:

Always measure the room accurately to avoid purchasing excess or insufficient material. Consider the placement of entrances, doors, and obstacles within the room to ensure a smooth installation process. Take note of the direction of the carpet's pattern to enhance the overall aesthetic appeal of your room.

For more information on home improvement projects and the science behind materials, stay updated with our blog. Happy recarpeting!