Find the fourth proportional to 12, 18, 20

Options

A. 30
B. 50
C. 35
D. 40

Answer

To find the fourth proportional to the numbers 12, 18, and 20, we can use the concept of proportionality. The fourth proportional \( x \) can be found using the formula:

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

Where:
- \( a = 12 \)
- \( b = 18 \)
- \( c = 20 \)

### Step-by-Step Solution:

1. **Set up the proportion**:
We can set up the equation based on the definition of proportionality:
\[ \frac{12}{18} = \frac{20}{x} \]

2. **Cross-multiply**:
Cross-multiplying gives us:
\[ 12 \cdot x = 18 \cdot 20 \]

3. **Calculate the right side**:
Now calculate \( 18 \cdot 20 \):
\[ 18 \cdot 20 = 360 \]

4. **Substitute back into the equation**:
Substitute back into the equation:
\[ 12x = 360 \]

5. **Solve for \( x \)**:
Divide both sides by 12 to isolate \( x \):
\[ x = \frac{360}{12} \]

6. **Calculate the value of \( x \)**:
Now calculate \( \frac{360}{12} \):
\[ x = 30 \]

### Final Answer:
The fourth proportional to 12, 18, and 20 is **30**.