Choose the correct answer from the alternatives given :
If $x : v :: 1 : 3 : 5$ then value of $\frac{\sqrt{x^{2} + 7 y^{2} + 9 z^{2}}}{x}$ is

7

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17

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13

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1

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Solution

The correct option is D $17$
Let $x, y a n d z$ be $k, 3 k a n d 5 k$ respectively.
Putting the value in the equation,
$\Rightarrow \frac{\sqrt{k^{2} + 7 \times (3 k)^{2} + 9 (5 k)^{2}}}{k}$
$\Rightarrow \frac{\sqrt{k^{2} + 63 k^{2} + 225 k^{2}}}{k}$
$\Rightarrow \frac{\sqrt{289 k^{2}}}{k}$
$\frac{17 k}{k}$
$= 17$

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