If $\sqrt{6}:x:: \sqrt{3}: (1+\sqrt{2})$, then $x$ is equal to

$\sqrt{2}+2$

The correct answer is Option (1) → $\sqrt{2}+2$

Given the analogy:

$\sqrt{6} : x :: \sqrt{3} : (1+\sqrt{2})$

This means:

$\frac{\sqrt{6}}{x} = \frac{\sqrt{3}}{1+\sqrt{2}}$

So,

$x = \frac{\sqrt{6}(1+\sqrt{2})}{\sqrt{3}}$

Since

$\frac{\sqrt{6}}{\sqrt{3}} = \sqrt{2}$

$x = \sqrt{2}(1+\sqrt{2}) = \sqrt{2} + 2$