If 9, x, x, 49 are in proportion, find the value of x.

Answer

To solve the problem where 9, x, x, and 49 are in proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Proportion**: We know that if four numbers are in proportion, then the ratio of the first two numbers is equal to the ratio of the last two numbers. This can be expressed as:
\[ \frac{9}{x} = \frac{x}{49} \]

2. **Cross-Multiply**: To eliminate the fractions, we can cross-multiply:
\[ 9 \cdot 49 = x \cdot x \]
This simplifies to:
\[ 441 = x^2 \]

3. **Solve for x**: To find the value of x, we need to take the square root of both sides:
\[ x = \sqrt{441} \]

4. **Calculate the Square Root**: Now, we calculate the square root of 441:
\[ x = 21 \]

5. **Conclusion**: Therefore, the value of x is:
\[ x = 21 \]

### Summary:
The value of x is 21.

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