If `9 xx 3 = 36, 11 xx 7 = 81` , then What is the value of `5 xx 13?`

Options

A. 65
B. 66
C. 81
D. 51

Explanation

To solve the problem, we need to identify the pattern used in the given equations and then apply it to find the value of \(5 \times 13\).

### Step-by-Step Solution:

1. **Identify the Pattern**:
- We have two equations:
- \(9 \times 3 = 36\)
- \(11 \times 7 = 81\)
- We need to find a consistent rule that applies to both equations.

2. **Calculate the Average**:
- For the first equation \(9 \times 3\):
- Calculate the average:
\[ \text{Average} = \frac{9 + 3}{2} = \frac{12}{2} = 6 \]
- Now, square the average:
\[ 6^2 = 36 \]
- This matches the right-hand side of the first equation.

3. **Verify the Second Equation**:
- For the second equation \(11 \times 7\):
- Calculate the average:
\[ \text{Average} = \frac{11 + 7}{2} = \frac{18}{2} = 9 \]
- Now, square the average:
\[ 9^2 = 81 \]
- This matches the right-hand side of the second equation.

4. **Apply the Same Rule to \(5 \times 13\)**:
- Calculate the average:
\[ \text{Average} = \frac{5 + 13}{2} = \frac{18}{2} = 9 \]
- Now, square the average:
\[ 9^2 = 81 \]

5. **Conclusion**:
- Therefore, the value of \(5 \times 13\) is \(81\).

### Final Answer:
\[ 5 \times 13 = 81 \]