Find the `4^(th)` proportional to 9,17 and 27.

Options

A. a. 57
B. b. 48
C. c. 51
D. d. 53

Answer

To find the 4th proportional to the numbers 9, 17, and 27, we can follow these steps:

### Step 1: Set up the proportion
We denote the 4th proportional as \( x \). The relationship can be expressed as:
\[ \frac{9}{17} = \frac{27}{x} \]

### Step 2: Cross-multiply
Cross-multiplying gives us:
\[ 9x = 27 \times 17 \]

### Step 3: Calculate \( 27 \times 17 \)
Now, we need to compute \( 27 \times 17 \):
\[ 27 \times 17 = 459 \]
So, we have:
\[ 9x = 459 \]

### Step 4: Solve for \( x \)
To find \( x \), we divide both sides by 9:
\[ x = \frac{459}{9} \]

### Step 5: Perform the division
Now, we calculate \( \frac{459}{9} \):
\[ 459 \div 9 = 51 \]
Thus, we find:
\[ x = 51 \]

### Conclusion
The 4th proportional to 9, 17, and 27 is \( 51 \).

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