Question : Three numbers are in the ratio 2 : 3 : 4. If the sum of their squares is 1856, the numbers are:
Option 1: 8, 12, and 16
Option 2: 16, 24, and 32
Option 3: 12, 18, and 24
Option 4: None of the above.
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Correct Answer: 16, 24, and 32
Solution :
Given: Three numbers are in the ratio 2 : 3 : 4 and the sum of their squares is 1856.
Let the numbers be $2x, 3x,$ and $4x$.
According to the question,
(2$x$)
2
+ (3$x$)
2
+ (4$x$)
2
= 1856
⇒ 4$x$
2
+ 9$x$
2
+ 16$x$
2
= 1856
⇒ 29$x$
2
= 1856
⇒ $x$
2
= 64
$\therefore x$ = 8
So, the numbers are (8 × 2) = 16, (8 × 3) = 24, and (8 × 4) = 32.
Hence, the correct answer is "16, 24, and 32".
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