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.