https://file.aiquickdraw.com/mathbot/file/1730394671998vdcw40jq.jpg

Let's verify if your approach and equation are correct.

### Problem Summary
The rectangular picture frame has:
- Width \( w \)
- Length \( w + 3 \)
- Area of glass in the frame: \( 154 \, \text{cm}^2 \)

### Solution Verification

1. **Formulating the Area Equation:**
   The area \( A \) of a rectangle is given by:
   \[
   A = \text{length} \times \text{width}
   \]
   Substituting the given dimensions:
   \[
   154 = w \times (w + 3)
   \]

2. **Expanding the Equation:**
   Expanding \( w \times (w + 3) \):
   \[
   154 = w^2 + 3w
   \]

3. **Setting the Equation to Standard Form:**
   To set it to standard form, move 154 to the other side:
   \[
   0 = w^2 + 3w - 154
   \]

### Conclusion
Your equation, \( 0 = w^2 + 3w - 154 \), is correct and matches the standard form of a quadratic equation. 

Would you like further details on solving this quadratic equation?

---

Here are 5 related questions for deeper understanding:

1. How would you solve the equation \( w^2 + 3w - 154 = 0 \) for \( w \)?
2. What are the possible values of \( w \) if you solve the quadratic equation?
3. How does changing the dimensions \( w \) and \( w + 3 \) affect the area of the frame?
4. How could you verify the solutions to ensure they satisfy the original area equation?
5. What other methods could you use to solve a quadratic equation like this?

**Tip:** To solve a quadratic equation, consider using the quadratic formula: \( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 1 \), \( b = 3 \), and \( c = -154 \).

Verify the solution to determine the width of a rectangular picture frame with dimensions w and w + 3, given that the area of glass in the frame is 154 cm². This problem involves setting up and solving a quadratic equation, 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