If 36, x, 16 are in continued proportion, find the value of x.

Answer

To find the value of \( x \) when the numbers 36, \( x \), and 16 are in continued proportion, we can follow these steps:

### Step 1: Understand the concept of continued proportion
In continued proportion, if three numbers \( a \), \( b \), and \( c \) are in continued proportion, then the ratio \( \frac{a}{b} = \frac{b}{c} \).

### Step 2: Set up the equation
Given the numbers 36, \( x \), and 16, we can set up the equation based on the definition of continued proportion:
\[ \frac{36}{x} = \frac{x}{16} \]

### Step 3: Cross-multiply
Cross-multiplying gives us:
\[ 36 \cdot 16 = x \cdot x \]
This simplifies to:
\[ 576 = x^2 \]

### Step 4: Solve for \( x \)
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{576} \]
Calculating the square root:
\[ x = 24 \]

### Conclusion
The value of \( x \) is 24.

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