If 22, x, 88 are in a continued proportion, find the value of x.
A. 24 B. 33 C. 44 D. 36

Options

A. A
B. C
C. D
D. B

Answer

To find the value of \( x \) in the continued proportion \( 22, x, 88 \), we can follow these steps:

### Step-by-Step Solution

1. **Understanding Continued Proportion**:
If \( 22, x, 88 \) are in continued proportion, it means that the ratio of the first two terms is equal to the ratio of the last two terms. This can be expressed mathematically as:
\[ \frac{22}{x} = \frac{x}{88} \]

2. **Cross Multiplying**:
To eliminate the fractions, we can cross multiply:
\[ 22 \cdot 88 = x \cdot x \]
This simplifies to:
\[ x^2 = 22 \cdot 88 \]

3. **Calculating \( 22 \cdot 88 \)**:
We can calculate \( 22 \cdot 88 \):
\[ 22 \cdot 88 = 1936 \]
So, we have:
\[ x^2 = 1936 \]

4. **Finding \( x \)**:
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{1936} \]

5. **Calculating the Square Root**:
We can calculate the square root:
\[ x = 44 \]

6. **Conclusion**:
Therefore, the value of \( x \) is \( 44 \).

### Final Answer
The value of \( x \) is \( 44 \), which corresponds to option C.