The mean proportinal between 16 and 49 :

Options

A. 64
B. 144
C. 28
D. 49

Answer

To find the mean proportional between 16 and 49, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Mean Proportional**:
Let the mean proportional between 16 and 49 be denoted as \( x \). This means we can express the relationship as:
\[ \frac{16}{x} = \frac{x}{49} \]

2. **Cross-Multiply**:
To eliminate the fractions, we cross-multiply:
\[ 16 \cdot 49 = x \cdot x \]
This simplifies to:
\[ x^2 = 16 \cdot 49 \]

3. **Calculate the Product**:
Now we need to calculate \( 16 \cdot 49 \):
\[ 16 \cdot 49 = 784 \]
So, we have:
\[ x^2 = 784 \]

4. **Take the Square Root**:
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{784} \]

5. **Calculate the Square Root**:
Now, we calculate \( \sqrt{784} \):
\[ \sqrt{784} = 28 \]

6. **Conclusion**:
Therefore, the mean proportional between 16 and 49 is:
\[ x = 28 \]

### Final Answer:
The mean proportional between 16 and 49 is **28**.

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