Choose the set of numbers from the four alternative sets, which is similar to the given set.
Given set : (63, 49, 35)

Options

A. (72, 40, 24)
B. (72, 48, 24)
C. (64, 40, 28)
D. (81, 63, 45)

Explanation

To solve the problem, we need to identify a set of numbers that shares a similar relationship with the given set (63, 49, 35).

### Step-by-Step Solution:

1. **Identify the Given Set**: The given set of numbers is (63, 49, 35).

2. **Factor Each Number**:
- For 63:
\[ 63 = 7 \times 9 \]
- For 49:
\[ 49 = 7 \times 7 \]
- For 35:
\[ 35 = 7 \times 5 \]

3. **Identify the Common Factor**:
- From the factorizations, we can see that all three numbers share a common factor of 7.
- We can express them in terms of this common factor:
\[ 63 = 7 \times 9, \quad 49 = 7 \times 7, \quad 35 = 7 \times 5 \]
- This can be written as \( 7 \times (9, 7, 5) \).

4. **Look for Similar Sets**: Now we need to check the alternative sets provided in the options to find a set that has a similar structure (a common factor).

5. **Analyze Each Option**:
- **Option A**: (72, 40, 24)
- Factor:
- \( 72 = 8 \times 9 \)
- \( 40 = 8 \times 5 \)
- \( 24 = 8 \times 3 \)
- Common factor: 8 (not similar).

- **Option B**: (48, 36, 24)
- Factor:
- \( 48 = 12 \times 4 \)
- \( 36 = 12 \times 3 \)
- \( 24 = 12 \times 2 \)
- Common factor: 12 (not similar).

- **Option C**: (64, 40, 28)
- Factor:
- \( 64 = 16 \times 4 \)
- \( 40 = 8 \times 5 \)
- \( 28 = 4 \times 7 \)
- No common factor across all (not similar).

- **Option D**: (81, 63, 45)
- Factor:
- \( 81 = 9 \times 9 \)
- \( 63 = 7 \times 9 \)
- \( 45 = 9 \times 5 \)
- Common factor: 9 (similar structure).
- We can express this as:
\[ 81 = 9 \times 9, \quad 63 = 9 \times 7, \quad 45 = 9 \times 5 \]
- This can be written as \( 9 \times (9, 7, 5) \).

6. **Conclusion**: The set that is similar to the given set (63, 49, 35) is option D (81, 63, 45).

### Final Answer:
**Option D** is the correct answer.