the length and breadth of a rectangular metal sheet measured using meter ruler marked in mm are 20.0cm and 12.5cm respectively. Calculate the possible error in the perimeter of the metal sheet and the percentage error of the perimeter

### Step 1: Understand the measurements and potential error.
- Length (\( L \)): \( 20.0 \, \text{cm} \)
- Breadth (\( B \)): \( 12.5 \, \text{cm} \)
- The measurements are made using a meter ruler marked in millimeters (mm), meaning the smallest unit of measurement is \( 1 \, \text{mm} \) or \( 0.1 \, \text{cm} \).

The possible error in each measurement is \( \pm 0.1 \, \text{cm} \).

### Step 2: Calculate the perimeter.
The perimeter \( P \) of a rectangle is given by:
\[
P = 2(L + B)
\]
Substitute the given values:
\[
P = 2(20.0 \, \text{cm} + 12.5 \, \text{cm}) = 2 \times 32.5 \, \text{cm} = 65.0 \, \text{cm}
\]

### Step 3: Calculate the possible error in the perimeter.
The possible error in the perimeter (\( \Delta P \)) is given by the sum of the possible errors in the length and breadth:
\[
\Delta P = 2(\Delta L + \Delta B)
\]
Since the error in both length and breadth is \( 0.1 \, \text{cm} \):
\[
\Delta P = 2(0.1 \, \text{cm} + 0.1 \, \text{cm}) = 2 \times 0.2 \, \text{cm} = 0.4 \, \text{cm}
\]

### Step 4: Calculate the percentage error.
The percentage error in the perimeter is calculated by:
\[
\text{Percentage Error} = \left( \frac{\Delta P}{P} \right) \times 100\%
\]
Substitute the values:
\[
\text{Percentage Error} = \left( \frac{0.4 \, \text{cm}}{65.0 \, \text{cm}} \right) \times 100\% \approx 0.615\%
\]

### Final Answers:
- **Possible Error in Perimeter:** \( \pm 0.4 \, \text{cm} \)
- **Percentage Error in Perimeter:** \( \approx 0.615\% \)

Would you like further details or have any questions?

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Here are 5 related questions to explore:

1. How does the error change if the ruler's smallest unit is in centimeters instead of millimeters?
2. What would be the percentage error if the breadth was measured as 25.0 cm instead?
3. How does the percentage error in perimeter compare to the percentage error in the area?
4. What is the possible error in the area of the metal sheet?
5. How would rounding off measurements to the nearest cm impact the error in perimeter?

**Tip:** Always consider the smallest unit of measurement when calculating potential errors, as it directly affects accuracy.

Learn how to calculate the possible error and percentage error in the perimeter of a rectangle when measurements are made using a meter ruler marked in millimeters (mm). Includes step-by-step solution and calculations for a rectangle with dimensions 20.0cm x 12.5cm. Suitable for Grades 7-9.

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