Calculate the 3rd proportional to 15 and 30.

Options

A. 55
B. 15
C. 65
D. 60

Answer

To find the third proportional to the numbers 15 and 30, we can follow these steps:

### Step 1: Understand the Concept of Proportions
The third proportional to two numbers A and B is a number C such that the ratio A:B is equal to the ratio B:C. This can be expressed mathematically as:
\[ \frac{A}{B} = \frac{B}{C} \]

### Step 2: Assign the Values
In this case, we have:
- A = 15
- B = 30
- C = ? (this is what we need to find)

### Step 3: Set Up the Proportion
Using the values we have, we can set up the proportion:
\[ \frac{15}{30} = \frac{30}{C} \]

### Step 4: Cross Multiply
To solve for C, we cross multiply:
\[ 15 \cdot C = 30 \cdot 30 \]

### Step 5: Calculate the Right Side
Now, calculate the right side:
\[ 30 \cdot 30 = 900 \]
So we have:
\[ 15 \cdot C = 900 \]

### Step 6: Solve for C
Now, to find C, divide both sides by 15:
\[ C = \frac{900}{15} \]

### Step 7: Perform the Division
Calculating the division:
\[ C = 60 \]

### Conclusion
Thus, the third proportional to 15 and 30 is **60**.

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