If `(sqrt(1296))/(x)=(x)/(2.25)`, then find the value of x.

Options

A. 6
B. 8
C. 7
D. 9

Answer

To solve the equation \(\frac{\sqrt{1296}}{x} = \frac{x}{2.25}\), we will follow these steps:

### Step 1: Calculate the square root of 1296
First, we need to find \(\sqrt{1296}\).

\[ \sqrt{1296} = 36 \]

### Step 2: Substitute the square root back into the equation
Now we can substitute this value back into the equation:

\[ \frac{36}{x} = \frac{x}{2.25} \]

### Step 3: Cross-multiply to eliminate the fractions
Next, we cross-multiply to eliminate the fractions:

\[ 36 \cdot 2.25 = x \cdot x \]

This simplifies to:

\[ 36 \cdot 2.25 = x^2 \]

### Step 4: Calculate \(36 \cdot 2.25\)
Now we calculate \(36 \cdot 2.25\):

\[ 36 \cdot 2.25 = 36 \cdot \frac{225}{100} = \frac{36 \cdot 225}{100} \]

Calculating \(36 \cdot 225\):

\[ 36 \cdot 225 = 8100 \]

So,

\[ \frac{8100}{100} = 81 \]

Thus, we have:

\[ x^2 = 81 \]

### Step 5: Take the square root of both sides
Now we take the square root of both sides to solve for \(x\):

\[ x = \sqrt{81} = 9 \]

### Conclusion
Therefore, the value of \(x\) is:

\[ \boxed{9} \]

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