If `(x)/(16)=(196)/(x)` , then value of `|x|` is

Options

A. 28
B. 36
C. 52
D. 56

Explanation

To solve the equation \(\frac{x}{16} = \frac{196}{x}\), we will follow these steps:

### Step 1: Cross-multiply the equation
We start with the given equation:
\[ \frac{x}{16} = \frac{196}{x} \]
Cross-multiplying gives us:
\[ x \cdot x = 196 \cdot 16 \]
This simplifies to:
\[ x^2 = 196 \cdot 16 \]

### Step 2: Calculate \(196 \cdot 16\)
Next, we need to calculate \(196 \cdot 16\):
\[ 196 \cdot 16 = 3136 \]
So we now have:
\[ x^2 = 3136 \]

### Step 3: Take the square root of both sides
To find \(x\), we take the square root of both sides:
\[ x = \pm \sqrt{3136} \]

### Step 4: Calculate \(\sqrt{3136}\)
Now we calculate \(\sqrt{3136}\):
\[ \sqrt{3136} = 56 \]
Thus, we have:
\[ x = \pm 56 \]

### Step 5: Find the absolute value \(|x|\)
Finally, we need to find the absolute value of \(x\):
\[ |x| = 56 \]

### Final Answer
The value of \(|x|\) is:
\[ \boxed{56} \]