What is the third proportional to 10 and 30?

Options

A. 90
B. 25
C. 50
D. 40

Answer

To find the third proportional to the numbers 10 and 30, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Third Proportional**:
Let the third proportional to 10 and 30 be denoted as \( x \).

2. **Set Up the Proportion**:
The relationship for the third proportional can be expressed as:
\[ \frac{10}{30} = \frac{30}{x} \]

3. **Cross Multiply**:
Cross multiplying gives us:
\[ 10 \cdot x = 30 \cdot 30 \]

4. **Calculate the Right Side**:
Calculate \( 30 \cdot 30 \):
\[ 30 \cdot 30 = 900 \]
So, we have:
\[ 10x = 900 \]

5. **Solve for \( x \)**:
Divide both sides by 10 to isolate \( x \):
\[ x = \frac{900}{10} \]
Simplifying this gives:
\[ x = 90 \]

6. **Conclusion**:
Therefore, the third proportional to 10 and 30 is \( 90 \).

### Final Answer:
The third proportional to 10 and 30 is **90**.

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