A rectangular piece of carpet has dimensions of 6 feet by 8 feet. A larger rectangular piece of carpet has dimensions that are 
 
 times longer. What area, in square feet, does the larger piece of carpet cover?

Let's solve this step by step.

The original rectangular carpet has dimensions of 6 feet by 8 feet.

The problem mentions a "larger rectangular piece of carpet" that has dimensions that are "times longer." Since the word "times" suggests multiplication, but no specific multiplier is given, I'll assume you're asking for a general solution based on some multiplier $ x $, which we'll substitute later if needed.

### Step 1: Area of the original carpet
The area $ A $ of a rectangle is calculated by multiplying its length and width:
\[
A = \text{length} \times \text{width} = 6 \times 8 = 48 \text{ square feet}.
\]

### Step 2: Dimensions of the larger carpet
If the larger carpet is $ x $ times longer, both dimensions (length and width) will be multiplied by $ x $. So, the new dimensions will be:
\[
\text{New length} = 6x, \quad \text{New width} = 8x.
\]

### Step 3: Area of the larger carpet
The area of the larger carpet is:
\[
A_{\text{larger}} = (\text{new length}) \times (\text{new width}) = (6x) \times (8x) = 48x^2 \text{ square feet}.
\]

### Conclusion:
The area of the larger carpet is $ 48x^2 $ square feet, where $ x $ is the factor by which the dimensions are scaled.

If you provide the specific multiplier $ x $, I can give you the exact area.

Would you like any additional details or clarifications?

Here are 5 related questions for further exploration:
1. If the larger carpet's dimensions are 3 times longer, what is the area?
2. What is the perimeter of the original carpet?
3. How much larger is the area of the bigger carpet compared to the original?
4. If the larger carpet costs $5 per square foot, what would be the total cost?
5. What would be the diagonal length of the original and larger carpets?

**Tip:** When scaling dimensions of a rectangle, the area increases by the square of the scaling factor.

A rectangular piece of carpet has dimensions of 6 feet by 8 feet. A larger rectangular piece of carpet has dimensions that are times longer. What area, in square feet, does the larger piece of carpet cover?

Learn how to calculate the area of a larger rectangular carpet when its dimensions are scaled by a factor. This problem uses concepts of geometry and algebra to find the area of the larger carpet based on the original dimensions of 6 feet by 8 feet. Suitable for students in Grades 6-8.

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