If 8:x=x:18 then x is equal to

Options

A. 144
B. 72
C. 26
D. 12

Answer

To solve the equation \( \frac{8}{x} = \frac{x}{18} \), we can follow these steps:

### Step 1: Set up the equation
We start with the given ratio:
\[ \frac{8}{x} = \frac{x}{18} \]

### Step 2: Cross-multiply
To eliminate the fractions, we can cross-multiply:
\[ 8 \cdot 18 = x \cdot x \]
This simplifies to:
\[ 144 = x^2 \]

### Step 3: Solve for \( x \)
Now, we need to find \( x \) by taking the square root of both sides:
\[ x = \sqrt{144} \]
Calculating the square root gives us:
\[ x = 12 \]

### Conclusion
Thus, the value of \( x \) is:
\[ \boxed{12} \]

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