Question

Suppose a, b, c are real numbers such that a:b:c = 3:2:4. Then $\sqrt{a^2 + 6b^2 + c^2}$ is equal to: }

• A. a + 3b
• B. a + 2b
• C. b + c
• D. a + b + c

Hint:

Plug in the ratio values directly to see which option matches the result.

Answer 1

The Correct Option is B

Step 1: Concept
Ratio substitution in expressions.

Step 2: Analysis
Let $a=3k, b=2k, c=4k$.

Step 3: Calculation
$\sqrt{(3k)^2 + 6(2k)^2 + (4k)^2} = \sqrt{9k^2 + 24k^2 + 16k^2} = \sqrt{49k^2} = 7k$.
Check options:
(B) $a + 2b = 3k + 2(2k) = 7k$.

Step 4: Conclusion
The expression equals $a + 2b$. Final Answer: (B)