The third proportional to 9 and 12 is

Options

A. 10.5
B. 8
C. 16
D. 21

Answer

To find the third proportional to the numbers 9 and 12, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Third Proportional**:
The third proportional to two numbers \( A \) and \( B \) is a number \( C \) such that the ratio of \( A \) to \( B \) is equal to the ratio of \( B \) to \( C \). This can be expressed as:
\[ \frac{A}{B} = \frac{B}{C} \]

2. **Assigning Values**:
Here, let \( A = 9 \) and \( B = 12 \). We need to find \( C \).

3. **Setting Up the Equation**:
According to the definition, we can write:
\[ \frac{9}{12} = \frac{12}{C} \]

4. **Cross-Multiplying**:
To eliminate the fractions, we cross-multiply:
\[ 9 \times C = 12 \times 12 \]

5. **Calculating the Right Side**:
Now, calculate \( 12 \times 12 \):
\[ 12 \times 12 = 144 \]
So the equation becomes:
\[ 9C = 144 \]

6. **Solving for \( C \)**:
Now, divide both sides by 9 to solve for \( C \):
\[ C = \frac{144}{9} \]

7. **Calculating \( C \)**:
Now perform the division:
\[ C = 16 \]

8. **Conclusion**:
Therefore, the third proportional to 9 and 12 is \( 16 \).

### Final Answer:
The third proportional to 9 and 12 is **16**.

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