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

18,27,36

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16,24,32

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12,18,24

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2,3,4

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Solution

The correct option is B 16,24,32
Let the numbers be a, b, c then a:b:c = 2:3:4 and $a^{2} + b^{2} + c^{2} = 1856$
Let a=2k,b=3k,c=4k
$\Rightarrow 4 k^{2} + 9 k^{2} + 16 k^{2} = 1856$
$\Rightarrow k = \sqrt{64} = 8$
So, a = 16 , b = 24 , c = 32

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Similar questions

Three positive numbers are in the ratio $\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$ . Find the numbers if the sum iof their squares is 244.

3 : 2 : 5

1862

\frac{1}{2} : \frac{1}{3} : \frac{1}{4}

244

\frac{1}{2} : \frac{1}{3} : \frac{1}{4}

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