The third propotional to 9 and 15 is:

Options

A. 18
B. 36
C. 27
D. 25

Answer

To find the third proportional to 9 and 15, 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 \( x \) such that the ratio \( a:b \) is equal to the ratio \( b:x \).

### Step 2: Set up the proportion
Let the third proportional be \( x \). We can express the relationship as:
\[ \frac{9}{15} = \frac{15}{x} \]

### Step 3: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 9 \cdot x = 15 \cdot 15 \]

### Step 4: Simplify the equation
Calculating the right side:
\[ 15 \cdot 15 = 225 \]
So we have:
\[ 9x = 225 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 9:
\[ x = \frac{225}{9} \]

### Step 6: Perform the division
Calculating \( \frac{225}{9} \):
\[ 225 \div 9 = 25 \]

### Conclusion
Thus, the third proportional to 9 and 15 is:
\[ \boxed{25} \]

---