Based on the analogy given, find the missing pair from the given options.
`(3)/(5)` : 34 :: …… : …….
A. `(3)/(7) : 54`
B. `(4)/(7) : 65`
C. `(3)/(11) : 140`
D. `(4)/(9) : 87`

Options

A. C
B. A
C. D
D. B

Answer

To solve the problem, we need to find the missing pair that maintains the same relationship as the given pair `(3)/(5) : 34`.

### Step-by-Step Solution:

1. **Identify the relationship in the given pair**:
The pair `(3)/(5)` corresponds to the number `34`. We need to find out how these two numbers relate to each other.

- Calculate the squares of the numbers in the fraction:
\[ 3^2 + 5^2 = 9 + 25 = 34 \]
This shows that the sum of the squares of the numerator and denominator equals `34`.

2. **Check the options**:
We will check each option to see if the sum of the squares of the numbers in the fraction equals the corresponding number.

**Option A**: `(3)/(7) : 54`
- Calculate:
\[ 3^2 + 7^2 = 9 + 49 = 58 \quad (\text{not } 54) \]

**Option B**: `(4)/(7) : 65`
- Calculate:
\[ 4^2 + 7^2 = 16 + 49 = 65 \quad (\text{matches}) \]

**Option C**: `(3)/(11) : 140`
- Calculate:
\[ 3^2 + 11^2 = 9 + 121 = 130 \quad (\text{not } 140) \]

**Option D**: `(4)/(9) : 87`
- Calculate:
\[ 4^2 + 9^2 = 16 + 81 = 97 \quad (\text{not } 87) \]

3. **Conclusion**:
The only option that satisfies the same relationship as the original pair is **Option B**: `(4)/(7) : 65`.

### Final Answer:
**Option B: `(4)/(7) : 65`**