What is 4th proportional in 9, 13 and 153?

Options

A. a. 251
B. b. 181
C. c. 175
D. d. 221

Answer

To find the 4th proportional of the numbers 9, 13, and 153, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of 4th Proportional**:
The 4th proportional to three numbers \( A, B, C \) is a number \( D \) such that:
\[ \frac{A}{B} = \frac{C}{D} \]
Rearranging this gives us:
\[ D = \frac{C \cdot B}{A} \]

2. **Assign Values**:
Here, we have:
- \( A = 9 \)
- \( B = 13 \)
- \( C = 153 \)

3. **Substituting the Values into the Formula**:
Now, substituting the values into the formula for \( D \):
\[ D = \frac{153 \cdot 13}{9} \]

4. **Calculating the Numerator**:
First, calculate the product of \( 153 \) and \( 13 \):
\[ 153 \cdot 13 = 1989 \]

5. **Dividing by \( A \)**:
Now, divide \( 1989 \) by \( 9 \):
\[ D = \frac{1989}{9} \]

6. **Performing the Division**:
Performing the division:
\[ 1989 \div 9 = 221 \]

7. **Conclusion**:
Therefore, the 4th proportional of \( 9, 13, \) and \( 153 \) is:
\[ D = 221 \]

### Final Answer:
The 4th proportional of \( 9, 13, \) and \( 153 \) is \( 221 \).

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