`((?)/(18)) xx ((?)/(162))=1`

Options

A. 9
B. 18
C. 54
D. 36

Answer

To solve the equation \(\frac{x}{18} \times \frac{x}{162} = 1\), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{x}{18} \times \frac{x}{162} = 1 \]

### Step 2: Multiply the fractions
When multiplying fractions, we multiply the numerators together and the denominators together:
\[ \frac{x \times x}{18 \times 162} = 1 \]
This simplifies to:
\[ \frac{x^2}{2916} = 1 \]

### Step 3: Cross-multiply
To eliminate the fraction, we can cross-multiply:
\[ x^2 = 2916 \]

### Step 4: Solve for \(x\)
To find \(x\), we take the square root of both sides:
\[ x = \sqrt{2916} \]

### Step 5: Calculate the square root
Now we need to calculate \(\sqrt{2916}\). We can factor \(2916\) to find its square root:
\[ 2916 = 54^2 \]
Thus,
\[ x = 54 \]

### Final Answer
The value of \(x\) is:
\[ \boxed{54} \]