The length and breadth of a rectangular are 25 cm and 10 cm respectively and were measured to an accuracy of 0.1 cm. The percentage error in area is

Options

A. `2.8%`
B. `0.5%`
C. `1.4%`
D. `3%`

Answer

To find the percentage error in the area of a rectangle given its length and breadth along with their respective measurement accuracies, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Length (L) = 25 cm
- Breadth (B) = 10 cm
- Accuracy of measurement (ΔL and ΔB) = 0.1 cm

2. **Calculate the Actual Area (A):**
\[ A = L \times B = 25 \, \text{cm} \times 10 \, \text{cm} = 250 \, \text{cm}^2 \]

3. **Determine the Absolute Errors in Length and Breadth:**
- Absolute error in length (ΔL) = 0.1 cm
- Absolute error in breadth (ΔB) = 0.1 cm

4. **Calculate the Relative Errors:**
- Relative error in length:
\[ \frac{\Delta L}{L} = \frac{0.1 \, \text{cm}}{25 \, \text{cm}} = 0.004 \]
- Relative error in breadth:
\[ \frac{\Delta B}{B} = \frac{0.1 \, \text{cm}}{10 \, \text{cm}} = 0.01 \]

5. **Combine the Relative Errors to Find the Relative Error in Area:**
- The formula for the relative error in area (ΔA/A) is:
\[ \frac{\Delta A}{A} = \frac{\Delta L}{L} + \frac{\Delta B}{B} \]
Substituting the values:
\[ \frac{\Delta A}{A} = 0.004 + 0.01 = 0.014 \]

6. **Calculate the Percentage Error in Area:**
\[ \text{Percentage Error} = \left(\frac{\Delta A}{A}\right) \times 100 = 0.014 \times 100 = 1.4\% \]

### Final Answer:
The percentage error in the area of the rectangle is **1.4%**.

---