The sum of the squares of three numbers which are in the ratio $2 : 3 : 4$ is $725.$ What are these numbers?

10, 15, 20

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14, 21, 28

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20, 15, 30

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20, 30, 40

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Solution

The correct option is A $10, 15, 20$
Let the three numbers be 2x, 3x and 4x.
Given, $(2 x)^{2} + (3 x)^{2} + (4 x)^{2} = 725$
$\Rightarrow 4 x^{2} + 9 x^{2} + 16 x^{2} = 725 \Rightarrow 29 x^{2} = 725$
$\Rightarrow x^{2} = 25 \Rightarrow x = 5$
$∴$ The numbers are 10, 15 and 20.

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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.

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

244

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