The mean proportional between 9 and 16 is

Options

A. 12.5
B. 12
C. 5
D. none of these

Answer

To find the mean proportional between 9 and 16, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Mean Proportional**:
Let the mean proportional between 9 and 16 be denoted as \( x \).

2. **Set Up the Proportion**:
The mean proportional can be defined using the relationship:
\[ \frac{9}{x} = \frac{x}{16} \]

3. **Cross Multiply**:
To eliminate the fractions, we cross multiply:
\[ 9 \cdot 16 = x \cdot x \]
This simplifies to:
\[ 144 = x^2 \]

4. **Solve for \( x \)**:
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{144} \]

5. **Calculate the Square Root**:
The square root of 144 is:
\[ x = 12 \]

6. **Conclusion**:
Therefore, the mean proportional between 9 and 16 is:
\[ \text{Mean Proportional} = 12 \]