In each of the following questions , three statements of numbers following same rules are given . Find the rule and accordingly find the value of the number ?
`3 + 5 = 16, 7 + 9 = 64 , 10 + 12 = 121` , then 11 + 3 = ?

Options

A. 56
B. 48
C. 49
D. 196

Explanation

To solve the problem, we need to identify the pattern used in the given equations. Let's analyze the provided statements step by step.

### Step 1: Analyze the first equation
The first equation is:
\[ 3 + 5 = 16 \]

- Normally, \( 3 + 5 = 8 \).
- To get from 8 to 16, we can see that \( 16 = (8 \div 2)^2 \).
- So, we divide the sum by 2 and then square it.

### Step 2: Verify the pattern with the second equation
The second equation is:
\[ 7 + 9 = 64 \]

- Normally, \( 7 + 9 = 16 \).
- Applying the same rule: \( 16 \div 2 = 8 \) and then \( 8^2 = 64 \).
- This confirms that the pattern holds.

### Step 3: Verify the pattern with the third equation
The third equation is:
\[ 10 + 12 = 121 \]

- Normally, \( 10 + 12 = 22 \).
- Applying the rule: \( 22 \div 2 = 11 \) and then \( 11^2 = 121 \).
- This confirms that the pattern is consistent.

### Step 4: Apply the rule to the new equation
Now we need to find the value of:
\[ 11 + 3 = ? \]

- Normally, \( 11 + 3 = 14 \).
- Applying the rule: \( 14 \div 2 = 7 \) and then \( 7^2 = 49 \).

### Final Answer
Thus, the value of \( 11 + 3 \) according to the established rule is:
\[ 11 + 3 = 49 \]

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