If 27, 36, x are in continued proportion, find the value of x.

Answer

To find the value of \( x \) when the numbers 27, 36, and \( x \) are in continued proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Continued Proportion**:
- If \( a, b, c \) are in continued proportion, then the relationship can be expressed as:
\[ \frac{a}{b} = \frac{b}{c} \]
- In this case, let \( a = 27 \), \( b = 36 \), and \( c = x \).

2. **Setting Up the Equation**:
- Substitute the values into the proportion:
\[ \frac{27}{36} = \frac{36}{x} \]

3. **Cross Multiplying**:
- Cross multiply to eliminate the fractions:
\[ 27 \cdot x = 36 \cdot 36 \]

4. **Calculating \( 36 \cdot 36 \)**:
- Calculate \( 36^2 \):
\[ 36 \cdot 36 = 1296 \]
- So the equation now is:
\[ 27x = 1296 \]

5. **Solving for \( x \)**:
- Divide both sides by 27 to isolate \( x \):
\[ x = \frac{1296}{27} \]

6. **Calculating \( \frac{1296}{27} \)**:
- Perform the division:
\[ x = 48 \]

### Final Answer:
Thus, the value of \( x \) is \( 48 \).

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