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The problem presented involves finding how many meters of wire are needed to enclose a vegetable garden. The given conditions are as follows:

- The area of the vegetable garden is 80 m².
- The shape of the garden has one side marked as \(x + 2\) and another side marked as \(x\).
- A 1-meter wide iron net fence is to be built around the perimeter of the garden.

### Approach:

1. **Calculate dimensions:**
   - The area \(A\) of the garden is given by the formula for the area of a rectangle, which is:
     \[
     A = \text{Length} \times \text{Width}
     \]
   - The length and width are \(x + 2\) and \(x\), respectively. Hence:
     \[
     A = (x + 2) \times x = 80 \, \text{m}^2
     \]
     Expanding the equation:
     \[
     x^2 + 2x = 80
     \]
     Solving the quadratic equation:
     \[
     x^2 + 2x - 80 = 0
     \]

2. **Solve the quadratic equation:**
   We can solve \(x^2 + 2x - 80 = 0\) using the quadratic formula:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   where \(a = 1\), \(b = 2\), and \(c = -80\).

3. **Find the perimeter:**
   Once \(x\) is determined, we can calculate the perimeter \(P\) of the rectangle:
   \[
   P = 2 \times (\text{Length} + \text{Width}) = 2 \times ((x + 2) + x)
   \]

Let's proceed with solving the quadratic equation and find the perimeter of the garden.The value of \(x\) is 8 meters, which means the dimensions of the garden are:

- Width: \(x = 8 \, \text{m}\)
- Length: \(x + 2 = 10 \, \text{m}\)

The total perimeter of the garden is:
\[
P = 36 \, \text{meters}
\]

Thus, **36 meters** of wire are required to enclose the garden.

Would you like more details on any part of the solution or have any further questions?

Here are 5 related questions to expand your understanding:
1. How do we derive the quadratic formula for solving quadratic equations?
2. What would happen if the area of the garden was increased by 20%?
3. How do you find the perimeter for other shapes, like a circle or triangle?
4. Can we solve this problem graphically by plotting the quadratic equation?
5. How do the properties of quadratic functions help in real-life situations like this?

**Tip:** Always check the discriminant in a quadratic equation to determine if real solutions exist before applying the quadratic formula.

The area of the vegetable garden in the form shown in the figure was 80 m². A fence with a 1 m wide iron net was built around the green land. How many meters of wire are needed?

Solve a quadratic equation to determine the dimensions of a garden with an area of 80 m², and calculate the perimeter to find how much wire is needed. This solution covers concepts such as quadratic equations, the area of a rectangle, and perimeter calculation, suitable for Grades 8-10.

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