Find out a number which will satisfy both the blank spaces?
`(9^(2))/(?)=(?)/(9)`

Options

A. 81
B. 27
C. 9
D. 3

Explanation

To solve the equation \( \frac{9^2}{?} = \frac{?}{9} \), we will follow these steps:

### Step 1: Rewrite the equation
Let's denote the unknown number as \( x \). Therefore, we can rewrite the equation as:
\[ \frac{9^2}{x} = \frac{x}{9} \]

### Step 2: Substitute \( 9^2 \)
Calculate \( 9^2 \):
\[ 9^2 = 81 \]
Now substitute this value into the equation:
\[ \frac{81}{x} = \frac{x}{9} \]

### Step 3: Cross-multiply
To eliminate the fractions, we will cross-multiply:
\[ 81 \cdot 9 = x \cdot x \]
This simplifies to:
\[ 729 = x^2 \]

### Step 4: Solve for \( x \)
Now, we need to find \( x \) by taking the square root of both sides:
\[ x = \sqrt{729} \]

### Step 5: Calculate the square root
Calculating the square root:
\[ \sqrt{729} = 27 \]

### Final Answer
Thus, the number that satisfies both blank spaces is:
\[ \boxed{27} \]