If 36, 54, x are in continued proportion, find the value of x.

Options

A. 101
B. 81
C. 71
D. 91

Answer

To solve the problem where 36, 54, and x are in continued proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Continued Proportion**:
- If three numbers \( a, b, c \) are in continued proportion, then the ratio \( \frac{a}{b} = \frac{b}{c} \).
- In this case, we have \( a = 36 \), \( b = 54 \), and \( c = x \).

2. **Setting Up the Equation**:
- According to the definition, we can write:
\[ \frac{36}{54} = \frac{54}{x} \]

3. **Cross Multiplying**:
- To eliminate the fractions, we cross multiply:
\[ 36 \cdot x = 54 \cdot 54 \]

4. **Calculating \( 54 \cdot 54 \)**:
- Calculate \( 54 \cdot 54 \):
\[ 54 \cdot 54 = 2916 \]
- So, the equation now looks like:
\[ 36x = 2916 \]

5. **Solving for \( x \)**:
- To find \( x \), divide both sides by 36:
\[ x = \frac{2916}{36} \]

6. **Calculating \( \frac{2916}{36} \)**:
- Perform the division:
\[ x = 81 \]

### Final Answer:
Thus, the value of \( x \) is \( 81 \).

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