What Is the third proportional to 10 and 20 ?

Options

A. 30
B. 25
C. 50
D. 40

Answer

To find the third proportional to 10 and 20, we can follow these steps:

### Step 1: Understand the concept of third proportional
The third proportional to two numbers \( A \) and \( B \) (in this case, 10 and 20) is a number \( C \) such that the ratio of \( A \) to \( B \) is equal to the ratio of \( B \) to \( C \). This can be expressed mathematically as:

\[ \frac{A}{B} = \frac{B}{C} \]

### Step 2: Substitute the values
Here, \( A = 10 \) and \( B = 20 \). We can substitute these values into the equation:

\[ \frac{10}{20} = \frac{20}{C} \]

### Step 3: Cross-multiply
To solve for \( C \), we can cross-multiply:

\[ 10 \cdot C = 20 \cdot 20 \]

### Step 4: Calculate the right side
Now, calculate \( 20 \cdot 20 \):

\[ 20 \cdot 20 = 400 \]

So we have:

\[ 10C = 400 \]

### Step 5: Solve for \( C \)
Now, divide both sides by 10 to find \( C \):

\[ C = \frac{400}{10} = 40 \]

### Conclusion
Thus, the third proportional to 10 and 20 is \( C = 40 \).

---