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