In measuring the sides of a rectangle, errors of 5% and 3% in excess are made. The error per cent in the calculated area is 

Options

A. `8.35%`
B. `7.15%`
C. `8.15%`
D. `6.25%`

Answer

To find the error percentage in the calculated area of a rectangle when there are errors in measuring its sides, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Errors**:
- The error in measuring the length is 5% in excess.
- The error in measuring the breadth is 3% in excess.

2. **Represent the Length and Breadth**:
- Let the actual length of the rectangle be \( x \).
- Let the actual breadth of the rectangle be \( y \).

3. **Calculate the Measured Length**:
- The measured length with a 5% error is:
\[ \text{Measured Length} = x + 0.05x = 1.05x \]

4. **Calculate the Measured Breadth**:
- The measured breadth with a 3% error is:
\[ \text{Measured Breadth} = y + 0.03y = 1.03y \]

5. **Calculate the Actual Area**:
- The actual area of the rectangle without any error is:
\[ \text{Actual Area} = x \times y \]

6. **Calculate the Measured Area**:
- The measured area with the errors included is:
\[ \text{Measured Area} = (1.05x) \times (1.03y) = 1.0815xy \]

7. **Calculate the Error in Area**:
- The error in area is the difference between the measured area and the actual area:
\[ \text{Error in Area} = \text{Measured Area} - \text{Actual Area} = 1.0815xy - xy = 0.0815xy \]

8. **Calculate the Error Percentage**:
- The error percentage in the area can be calculated as:
\[ \text{Error Percentage} = \left( \frac{\text{Error in Area}}{\text{Actual Area}} \right) \times 100 = \left( \frac{0.0815xy}{xy} \right) \times 100 \]
- Simplifying this gives:
\[ \text{Error Percentage} = 0.0815 \times 100 = 8.15\% \]

### Final Answer:
The error percentage in the calculated area of the rectangle is **8.15%**.

---