If \(\sqrt{2}:(1+\sqrt{3})::\sqrt{6}:x\), then \(x\) is equal to:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(3+\sqrt{3}\)
The statement \(a:b::c:x\) says that the two ratios are equal, so the product of the extremes equals the product of the means: \(a\times x=b\times c\).
\(\sqrt{2}\times x=(1+\sqrt{3})\times\sqrt{6}\)
\(\displaystyle x=\frac{\sqrt{6}}{\sqrt{2}}(1+\sqrt{3})=\sqrt{3}(1+\sqrt{3})\)
\(x=\sqrt{3}+3=3+\sqrt{3}\)