10. This model shows the area of a garden. Write two expressions that represent the area.

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UpStudy AI · Accepted Answer

Certainly! To represent the area of a garden, we'll typically use the dimensions provided in the model. Assuming the garden is rectangular (a common shape for gardens), you can express the area using the length and width of the garden.

Let's define:
- **Length (L)**: The longer side of the garden.
- **Width (W)**: The shorter side of the garden.

### Expression 1:
**Area = Length × Width**

$$ \text{Area} = L \times W $$

### Expression 2:
**Area = Width × Length**

$$ \text{Area} = W \times L $$

*Note:* Both expressions are mathematically equivalent since multiplication is commutative (i.e., $$ L \times W = W \times L $$). However, depending on the context or how the garden's dimensions are presented, you might prefer one format over the other.

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### Example Scenario

**Given:**
- Length ($$ L $$) of the garden = 15 meters
- Width ($$ W $$) of the garden = 10 meters

**Calculations:**

1. **Using the first expression:**

$$ \text{Area} = L \times W = 15 \, \text{m} \times 10 \, \text{m} = 150 \, \text{m}^2 $$

2. **Using the second expression:**

$$ \text{Area} = W \times L = 10 \, \text{m} \times 15 \, \text{m} = 150 \, \text{m}^2 $$

Both expressions yield the same area of **150 square meters**.

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### Alternative Expressions

If the garden has a different shape or if additional information is provided, the expressions for the area might vary. For example:

- **Square Garden:**
  - If $$ s $$ is the side length, then:
    $$ \text{Area} = s^2 $$
  
- **Triangular Garden:**
  - If $$ b $$ is the base and $$ h $$ is the height, then:
    $$ \text{Area} = \frac{1}{2} \times b \times h $$

- **Circular Garden:**
  - If $$ r $$ is the radius, then:
    $$ \text{Area} = \pi r^2 $$

However, without specific details about the garden's shape beyond the initial assumption, the two expressions using length and width are the most straightforward representations.

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Feel free to provide more details or clarify the garden's shape if you need expressions tailored to a specific scenario!
Two expressions for the area of the garden are: 1. **Area = Length × Width** 2. **Area = Width × Length** These both represent the same area, depending on how the garden's dimensions are defined.

10. This model shows the area of a garden. Write two expressions that represent the area.

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