If three numbers are in the ratio $3 : 2 : 5$ and they are such that the sum of their squares is equal to $1, 862$ , the middle one is

11

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12

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13

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14

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Solution

The correct option is C $14$
Ratio given $: 3 : 2 : 5$
Let the numbers be $3 x, 2 x$ and $5 x$ respectively.
According to question,
${(3 x)}^{2} + {(2 x)}^{2} + {(5 x)}^{2} = 1862 \Rightarrow 9 x^{2} + 4 x^{2} + 25 x^{2} = 1862 \Rightarrow 38 x^{2} = 1862 \Rightarrow x^{2} = \frac{1862}{38} = 49 \Rightarrow x = \pm \sqrt[2]{49} = \pm 7 x = 7 x = - 7$
Middle no $= 2 x = 2 \times 7 = 14$

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