Three numbers are in the ratio 2 : 3 : 4. If the sum of

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Three numbers are in the ratio 2 : 3 : 4. If the sum of their squares is 1856, then the numbers are

1. 8, 12 and 16
2. 16, 24 and 32
3. 12, 18 and 24
4. None of the above

Correct Option: B

Numbers = 2x, 3x and 4x
∴ (2x)² + (3x)² + (4x)² = 1856
⇒ 4x² + 9x² +16x² = 1856
⇒ 29x² = 1856
⇒ x² = 1856 ÷ 29 = 64
∴ x = √64 = 8
∴ Numbers = 16, 24 and 32