Find the third proportional to 8 and 12

Answer

To find the third proportional to 8 and 12, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**:
The third proportional to two numbers \( A \) and \( B \) is a number \( C \) such that the ratio \( A : B \) is equal to the ratio \( B : C \). This can be expressed as:
\[ \frac{A}{B} = \frac{B}{C} \]

2. **Assign Values**:
Here, we have \( A = 8 \) and \( B = 12 \). We need to find \( C \) (which we will denote as \( X \)).

3. **Set Up the Equation**:
According to the proportionality, we can set up the equation:
\[ \frac{8}{12} = \frac{12}{X} \]

4. **Cross-Multiply**:
To eliminate the fractions, we cross-multiply:
\[ 8 \cdot X = 12 \cdot 12 \]

5. **Calculate the Right Side**:
Calculate \( 12 \cdot 12 \):
\[ 12 \cdot 12 = 144 \]
So, the equation becomes:
\[ 8X = 144 \]

6. **Solve for \( X \)**:
Now, divide both sides by 8 to find \( X \):
\[ X = \frac{144}{8} \]

7. **Perform the Division**:
Calculate \( \frac{144}{8} \):
\[ X = 18 \]

8. **Conclusion**:
Therefore, the third proportional to 8 and 12 is \( 18 \).