https://file.aiquickdraw.com/mathbot/file/1730755606329of11xyhx.jpg

To solve this problem, we need to find the possible length and width of a rectangle whose area is given by the expression \( x^2 + 4x \). The area \( A \) of a rectangle is calculated as the product of its length \( L \) and width \( W \):

\[
A = L \times W
\]

### Step 1: Factor the Area Expression
The area expression is \( x^2 + 4x \). We can factor this expression to find possible values for \( L \) and \( W \):

\[
x^2 + 4x = x(x + 4)
\]

This factorization suggests that the length and width could be \( x \) and \( x + 4 \), respectively.

### Step 2: Verify Against Answer Choices
Let's check which option matches this factorization:

1. **Option 1**: Length: \( x \), Width: \( x + 4 \)
2. **Option 2**: Length: \( x \), Width: \( x^2 + 4 \)
3. **Option 3**: Length: \( x^2 \), Width: \( 4x \)
4. **Option 4**: Length: \( x \), Width: \( 4x \)

Only **Option 1** (Length: \( x \); Width: \( x + 4 \)) correctly matches the factorization of \( x^2 + 4x \).

### Conclusion
The correct answer is:

**Option 1**: Length: \( x \); Width: \( x + 4 \).

Would you like a more detailed explanation or have any questions about the solution?

---

Here are some additional related questions you might find helpful:

1. How would the answer change if the area was \( x^2 - 4x \)?
2. What are other ways to find the factors of a quadratic expression like \( x^2 + 4x \)?
3. How do we handle cases where the area of a rectangle is a polynomial that doesn’t factor neatly?
4. What if the area was \( x^2 + 5x + 6 \)? How would we find possible length and width values?
5. How can we verify if the length and width values are positive, given different values of \( x \)?

**Tip:** When dealing with polynomials in geometry problems, factoring can often reveal useful dimensions that fit physical interpretations like length and width.

The area of a rectangle is x^2 + 4x. Which could be the length and width of the rectangle? (A = L x W)

Explore how to determine the possible length and width of a rectangle given the area x^2 + 4x. This problem demonstrates factoring quadratic expressions to solve for dimensions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation