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Three numbers are in the ratio of $3 : 5 : 9$ . Find the largest number, given the sum of the squares of the numbers is 460.

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answer is D.

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Detailed Solution

$\begin{array}{l} 3 : 5 : 9 \\ 3x, 5x, 9x \\ G i v e n {(3 x)}^{2} + {(5 x)}^{2} + {(9 x)}^{2} = 460 \\ 9 x^{2} + 25 x^{2} + 81 x^{2} = 460 \\ 115 x^{2} = 460 \\ x^{2} = 4 \\ x = 2 \\ ∴ largest number = 9 x \\ = 9 (2) = 18 \end{array}$

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