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In the sum of squares of 3 numbers which are in the ratio $2 : 3 : 4$ is $725$ then the numbers are

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10, 15, 20

14, 21, 28

20, 15, 30

20, 30, 40

answer is A.

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Detailed Solution

{(2 x)}^{2} + {(3 x)}^{2} + {(4 x)}^{2} = 725

$4 x^{2} + 9 x^{2} + 16 x^{2} = 725$

$29 x^{2} = 725$

$x^{2} = \frac{725}{29} = 25$

$x = \sqrt{25}$

$x = 5$

So numbers are $2 \times 5, 3 \times 5, 4 \times 5 = 10, 15, 20$

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