Find the value of x in each of the following :
` 16 : x : : x : 25`

Answer

To solve the problem \( 16 : x :: x : 25 \), we can follow these steps:

### Step 1: Understand the Proportion
The given proportion can be expressed mathematically as:
\[ \frac{16}{x} = \frac{x}{25} \]

### Step 2: Cross-Multiply
To eliminate the fractions, we cross-multiply:
\[ 16 \cdot 25 = x \cdot x \]
This simplifies to:
\[ 400 = x^2 \]

### Step 3: Solve for \( x \)
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{400} \]

### Step 4: Calculate the Square Root
Calculating the square root gives:
\[ x = 20 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{20} \]

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