Triangle : Hexagon
Geometry
Level
3
The perimeter of the equilateral triangle is twice the perimeter of the hexagon. What is the ratio of the area of the triangle to the hexagon?
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1 solution
Let the side of Equilateral Triangle be "a" and the side of Hexagon be "b".
Now, Perimeter of Triangle is twice the perimeter of Hexagon.
=> 3a = 2 × 6b.
=> a = 4b.
Now Area of Triangle = √3/4 × a^2 = √3/4 × (4b)^2 = 4√3 × b^2.
Also, Area of Hexagon = 6 × (Area of Equilateral Triangle with side b)
= 6 × √3/4 × b^2.
Hence, Required Ratio = (4√3 × b^2)/(6 × √3/4 × b^2) = 8/3.
Answer = 8/3.