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CAT 2021 Quant Question [Slot 1] with Solution 02

Question
If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is
  1. \(4\sqrt 6 \)
  2. \(6\sqrt 6 \)
  3. \(\sqrt 6 \)
  4. \(2\sqrt 6 \)
Option: 4
Solution:
Area of a regular hexagon = \(\frac{{3\sqrt 3 }}{2}{x^2}\) Area of an equilateral triangle = \(\frac{{\sqrt 3 }}{4}{\left( a \right)^2}\) ; where a = side of the triangle Since the area of the two figures are equal, we can equate them as folllows: \(\frac{{3\sqrt 3 }}{2}{x^2} = \frac{{\sqrt 3 }}{4}{\left( {12} \right)^2}\) On simplifying: \({x^2} = 24\;\) \(\therefore \;x = 2\sqrt 6 \)
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