Which number will replace both the question mark in `(361/? = ?/81)?`

Options

A. 191
B. 931
C. 171
D. None of these

Answer

To solve the equation \( \frac{361}{?} = \frac{?}{81} \), we can denote the question mark as \( x \). This gives us the equation:

\[ \frac{361}{x} = \frac{x}{81} \]

Now, we can cross-multiply to eliminate the fractions:

\[ 361 \cdot 81 = x \cdot x \]

This simplifies to:

\[ 361 \cdot 81 = x^2 \]

Next, we need to calculate \( 361 \cdot 81 \):

\[ 361 \cdot 81 = 29241 \]

So, we have:

\[ x^2 = 29241 \]

To find \( x \), we take the square root of both sides:

\[ x = \sqrt{29241} \]

Calculating the square root:

\[ x = 171 \]

Thus, the number that will replace both question marks is:

\[ \boxed{171} \]