A rectangular garden plot was measured as 155 cm by 50 cm. Determine the lower and upper bounds of it's perimeter. 

Be sure to explain your answer, and your work.

To calculate the **lower and upper bounds** of the perimeter of a rectangular garden plot, we need to first define the length and width measurements with their associated bounds.

### Step 1: Understand the bounds
When measurements are given to a certain precision, the values include some uncertainty. In this case, the garden plot’s dimensions are measured to the nearest centimeter:
- Length = 155 cm
- Width = 50 cm

Since the measurements are given to the nearest centimeter, the actual values could vary by up to ±0.5 cm. Therefore:
- The **lower bound** of a measurement is the value minus 0.5 cm.
- The **upper bound** of a measurement is the value plus 0.5 cm.

### Step 2: Calculate the bounds for length and width
For the **length**:
- Lower bound = \( 155 - 0.5 = 154.5 \) cm
- Upper bound = \( 155 + 0.5 = 155.5 \) cm

For the **width**:
- Lower bound = \( 50 - 0.5 = 49.5 \) cm
- Upper bound = \( 50 + 0.5 = 50.5 \) cm

### Step 3: Perimeter formula
The formula for the perimeter \( P \) of a rectangle is:

\[
P = 2(\text{length} + \text{width})
\]

### Step 4: Calculate the lower bound of the perimeter
The lower bound of the perimeter is calculated using the lower bounds of the length and width:
\[
P_{\text{lower}} = 2(154.5 + 49.5) = 2(204) = 408 \, \text{cm}
\]

### Step 5: Calculate the upper bound of the perimeter
The upper bound of the perimeter is calculated using the upper bounds of the length and width:
\[
P_{\text{upper}} = 2(155.5 + 50.5) = 2(206) = 412 \, \text{cm}
\]

### Final Answer:
- **Lower bound of the perimeter**: 408 cm
- **Upper bound of the perimeter**: 412 cm

### Explanation Summary:
The dimensions of the rectangle were measured to the nearest centimeter, leading to bounds of ±0.5 cm. We calculated the perimeter using these lower and upper bounds to ensure that the true perimeter lies between 408 cm and 412 cm.

Would you like further details, or do you have any questions?

### Related Questions:
1. How do you determine bounds for areas of a rectangle?
2. What happens if the garden plot is measured to the nearest millimeter instead of centimeter?
3. How do you calculate the uncertainty of the perimeter when dimensions are measured with higher precision?
4. Can the concept of bounds be applied to non-rectangular shapes, such as circles?
5. How does measurement error affect real-world construction and design projects?

### Tip:
Always consider measurement uncertainty in real-world problems, as even small variations can significantly impact the final result, especially for large-scale projects.

A rectangular garden plot was measured as 155 cm by 50 cm. Determine the lower and upper bounds of its perimeter. Be sure to explain your answer, and your work.

Learn how to calculate the lower and upper bounds of the perimeter of a rectangular garden plot measured as 155 cm by 50 cm, considering measurement uncertainty. This problem explains step-by-step perimeter calculations using the formula for a rectangle and discusses the impact of rounding to the nearest centimeter. Suitable for Grades 6-8.

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