If the third proportional to 7 and x is 28, find the value of x.

Answer

To find the value of \( x \) when the third proportional to 7 and \( x \) is 28, we can follow these steps:

### Step 1: Understand the concept of third proportional
The third proportional to two numbers \( A \) and \( B \) is a number \( C \) such that the ratio \( A:B = B:C \). In this case, we have \( A = 7 \), \( B = x \), and \( C = 28 \).

### Step 2: Set up the proportion
According to the definition of third proportional, we can set up the equation:
\[ \frac{7}{x} = \frac{x}{28} \]

### Step 3: Cross-multiply
Cross-multiplying gives us:
\[ 7 \cdot 28 = x \cdot x \]
which simplifies to:
\[ 196 = x^2 \]

### Step 4: Solve for \( x \)
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{196} \]
Calculating the square root, we find:
\[ x = 14 \]

### Conclusion
Thus, the value of \( x \) is \( 14 \).

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