Find the fourth proportional to 14, 28, and 21.

Options

A. 41
B. 42
C. 14
D. 40

Answer

To find the fourth proportional to the numbers 14, 28, and 21, we can set up a proportion based on the definition of fourth proportional. The fourth proportional \( x \) can be found using the relationship:

\[ \frac{a}{b} = \frac{c}{x} \]

Where:
- \( a = 14 \)
- \( b = 28 \)
- \( c = 21 \)

### Step-by-Step Solution:

1. **Set up the proportion**:
\[ \frac{14}{28} = \frac{21}{x} \]

2. **Cross-multiply**:
\[ 14 \cdot x = 28 \cdot 21 \]

3. **Calculate \( 28 \cdot 21 \)**:
\[ 28 \cdot 21 = 588 \]

4. **Substitute back into the equation**:
\[ 14x = 588 \]

5. **Solve for \( x \)**:
\[ x = \frac{588}{14} \]

6. **Perform the division**:
\[ x = 42 \]

Thus, the fourth proportional to 14, 28, and 21 is **42**.