https://file.aiquickdraw.com/mathbot/file/172618997028091ubajlr.jpg

From the image, the diagram shows a hydroponic plant greenhouse with a rectangular base. We are given the following information:

- The area of the rectangular base is \( 42 \, \text{m}^2 \).
- One dimension of the base is \( 7 \, \text{m} \) (length).
- The other dimension is \( x \, \text{m} \) (width).
- The height of the greenhouse is labeled as \( (x - 3) \, \text{m} \).

### Step-by-step approach:

1. **Determine the value of \( x \):**

   The area of a rectangle is given by:
   \[
   \text{Area} = \text{length} \times \text{width}
   \]
   In this case:
   \[
   42 = 7 \times x
   \]
   Solving for \( x \):
   \[
   x = \frac{42}{7} = 6
   \]

2. **Find the height of the greenhouse:**

   The height of the greenhouse is given as \( (x - 3) \, \text{m} \). Now that we know \( x = 6 \), we substitute:
   \[
   \text{Height} = 6 - 3 = 3 \, \text{m}
   \]

Thus, the height of the greenhouse is **3 meters**.

Would you like more details or have any questions? 

Here are five related questions you might find helpful:
1. How would the height change if the area of the base increased?
2. What is the volume of the greenhouse based on its height and dimensions?
3. How does the width of the base affect the overall structure of the greenhouse?
4. If the width was unknown, how would you find it if only the perimeter was given?
5. What are other possible shapes for the base of a greenhouse that could be efficient for space?

**Tip:** Always double-check the units when solving area and volume problems to ensure consistency in your calculations.

What is the height (in meters) of the greenhouse if the area of the base is 42 m², and the length of the base is 7 m?

This problem involves finding the height of a greenhouse based on the given area of 42 m² and a length of 7 meters. By applying basic geometry and algebra, students in Grades 5-7 can solve for the height with a step-by-step explanation.

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