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The problem states that the area of the flower bed is \( 5 \, \text{m}^2 \), and we need to find the value of \( x \).

### Given:
- The flower bed is in the shape of a square.
- Each side of the square is \( x \, \text{m} \), as indicated in the diagram.
- The outer dimensions of the flower bed and its surrounding are \( (x+1) \, \text{m} \).

### Steps:
1. **Area of the flower bed**: Since the flower bed is a square, the area of the square is given by:
   \[
   \text{Area of the flower bed} = x^2
   \]
   We are told that the area of the flower bed is \( 5 \, \text{m}^2 \), so:
   \[
   x^2 = 5
   \]

2. **Solving for \( x \)**:
   \[
   x = \sqrt{5}
   \]
   Since \( \sqrt{5} \approx 2.236 \), the value of \( x \) is approximately \( 2.236 \, \text{m} \).

Thus, the value of \( x \) is approximately \( 2.236 \, \text{m} \).

Would you like more details or explanations on any part of the process?

Here are 5 related questions to think about:
1. What is the perimeter of the flower bed given this value of \( x \)?
2. How much area is occupied by the border surrounding the flower bed?
3. If the area of the entire outer square (including the border) is given, how would you calculate it?
4. How would the area change if the side length of the flower bed increased by 1 meter?
5. What would be the value of \( x \) if the area of the flower bed were 9 square meters instead?

**Tip**: Remember that square roots of non-perfect squares are often irrational numbers, meaning they can't be expressed exactly as fractions.

In the figure, if the area of the flower-bed is 5 m², find the value of x.

Solve a geometry problem where you find the side length of a square flower-bed given its area. The problem involves the area formula for squares and solving quadratic equations. Suitable for Grades 8-10.

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