Question
Download Solution PDFThree numbers are in the ratio 2: 3: 4. If the sum of their squares is 1856, then the numbers are:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Three numbers are in the ratio 2:3:4.
The sum of their squares = 1856.
Calculations:
Let the numbers be 2x, 3x, and 4x.
Sum of squares = (2x)2 + (3x)2 + (4x)2.
1856 = (2x)2 + (3x)2 + (4x)2
⇒ 1856 = 4x2 + 9x2 + 16x2
⇒ 1856 = 29x2
⇒ x2 = 64
⇒ x = √64
⇒ x = 8
Therefore, the numbers are:
2x = 2 × 8 = 16
3x = 3 × 8 = 24
4x = 4 × 8 = 32
∴ The correct answer is option (2).
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