Find the third proportional to 6 and 12.

Options

A. 18
B. 9
C. 24
D. 15

Answer

To find the third proportional to the numbers 6 and 12, 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 of A to B is the same as the ratio of B to C. This can be expressed mathematically as:
\[ \frac{A}{B} = \frac{B}{C} \]

### Step 2: Set up the equation
Given A = 6 and B = 12, we can set up the equation:
\[ \frac{6}{12} = \frac{12}{C} \]

### Step 3: Cross-multiply to solve for C
Cross-multiplying gives us:
\[ 6 \cdot C = 12 \cdot 12 \]

### Step 4: Calculate the right side
Calculating the right side:
\[ 12 \cdot 12 = 144 \]
So the equation becomes:
\[ 6C = 144 \]

### Step 5: Solve for C
Now, divide both sides by 6 to find C:
\[ C = \frac{144}{6} = 24 \]

### Conclusion
The third proportional to 6 and 12 is 24.

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