https://file.aiquickdraw.com/mathbot/file/1727418800625r04hi8tf.jpg

The problem asks for the area of the room in square feet given its dimensions. According to the image, the room has:

- One side that measures **14 feet**.
- The other side has a length of **5 + 3c** feet.

To calculate the area of the room in square feet, we use the formula for the area of a rectangle:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Substituting the given dimensions:

\[
\text{Area} = 14 \times (5 + 3c)
\]

So, the area of the room is $ 14(5 + 3c) $ square feet.

Would you like help solving this expression for a specific value of $c$, or is there more you'd like to explore in this problem?

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**Related Questions:**
1. What happens to the area if $c = 1$?
2. How does changing the value of $c$ impact the total area?
3. What is the physical interpretation of the variable $c$ in this context?
4. Can the room area be expressed as a quadratic equation if we expand it further?
5. How much would the carpet cost if it is sold at $10 per square foot?

**Tip:** When dealing with variables in geometric problems, solve for one case at a time by assigning practical values to explore various scenarios.

If Mr. Arenth wants to put new carpeting in the room shown, how many square feet should he order?

Learn how to calculate the area of a room to order the correct amount of carpeting. In this problem, the room has dimensions of 14 feet and 5 + 3c feet. Using the area formula (Length × Width), the solution will show how to find the total square footage for carpeting. Suitable for Grades 6-8 students learning algebra and geometry concepts.

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