Exams › SSC CGL (Prelims) › General

An equilateral triangle and a regular hexagon enclose the same area. What is the ratio of the side of the triangle to the side of the hexagon?

1. 1 : sqrt(3)
2. 1 : sqrt(2)
3. sqrt(6) : 1
4. 1 : sqrt(1.5)

Correct answer: sqrt(6) : 1

Solution

Area of equilateral triangle = (sqrt 3 / 4)a^2 and area of regular hexagon = (3 sqrt 3 / 2)b^2. Equating gives a^2 = 6b^2, so a/b = sqrt(6), i.e. the ratio of sides is sqrt(6) : 1.

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