The ratio of three numbers is 2 : 3 : 6 and the sum of their squares is 441.…
2021
The ratio of three numbers is 2 : 3 : 6 and the sum of their squares is 441. What is the value of the largest of the three numbers?
Answer: C. 18 — Represent the numbers as 2x, 3x, and 6x based on the ratio 2 : 3 : 6. The sum of their squares is: (2x)² + (3x)² + (6x)² = 441. Simplify the equation: 4x² +…
- A.
54
- B.
27
- C.
18
- D.
21
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Correct answer: C
Represent the numbers as 2x, 3x, and 6x based on the ratio 2 : 3 : 6.
The sum of their squares is: (2x)² + (3x)² + (6x)² = 441.
Simplify the equation: 4x² + 9x² + 36x² = 441.
Combine terms: 49x² = 441.
Solve for x²: x² = 441 / 49 = 9.
Solve for x: x = 3.
The largest number is 6x = 6 * 3 = 18.
Final Answer: Option 3
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