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Geometry Questions

321. An equilateral triangle and a regular hexagon have equal perimeters. The ratio of the area of the triangle and that of the hexagon is ?

Correct Ans:2:3
Let x = side of triangle and y = side of regular hexagon
Given, 3x = 6y ? => x = 2y ?
Area of triangle = (?3/4) x^2
=> Area of hexagon = 6 X (?3/4) y^2 => 6 X (?3/4) * (x^2 /4) ----> Substituting y = x/2 => 3 (?3/8) x^2
=> Required ratio = (?3/4) x^2 : 3 (?3/8) x^2 = 2 : 3

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