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Mathematics

If 2:(1+3)::6:x\sqrt2:(1 + \sqrt3)::\sqrt6:x then value of x is:

  1. 3+3\sqrt3 + 3

  2. 131 - \sqrt3

  3. 33\sqrt3 - 3

  4. 1+31 + \sqrt3

Ratio Proportion

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Answer

Given,

2:(1+3)::6:x21+3=6xx=6(1+3)2x=3(1+3)x=3+3.\Rightarrow \sqrt2:(1 + \sqrt3)::\sqrt6:x \\[1em] \Rightarrow \dfrac{\sqrt{2}}{1 + \sqrt3} = \dfrac{\sqrt6}{x} \\[1em] \Rightarrow x = \dfrac{\sqrt6(1 + \sqrt3)}{\sqrt2} \\[1em] \Rightarrow x = \sqrt3(1 + \sqrt3) \\[1em] \Rightarrow x = \sqrt3 + 3.

Hence, option 1 is the correct option.

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