The third proportional to 9 and 12 is ?

Options

A. A) 14
B. B) 16
C. C) 18
D. D) 20

Answer

To find the third proportional to the numbers 9 and 12, we can follow these steps:

### Step 1: Set up the proportion
We know that if \( a \) and \( b \) are two numbers, the third proportional \( p \) can be found using the relationship:
\[ \frac{a}{b} = \frac{b}{p} \]
In this case, \( a = 9 \) and \( b = 12 \). Therefore, we can write:
\[ \frac{9}{12} = \frac{12}{p} \]

### Step 2: Cross-multiply
Cross-multiplying gives us:
\[ 9 \cdot p = 12 \cdot 12 \]

### Step 3: Simplify the equation
Calculating the right side:
\[ 9p = 144 \]

### Step 4: Solve for \( p \)
Now, divide both sides by 9 to find \( p \):
\[ p = \frac{144}{9} \]

### Step 5: Calculate \( p \)
Now, perform the division:
\[ p = 16 \]

Thus, the third proportional to 9 and 12 is **16**.

### Final Answer
The third proportional to 9 and 12 is **16**.

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