Question 58

An equilateral triangle and regular hexagon have the same perimeter. The ratio of the area of the triangle to that of the hexagon is

Solution

Let side of equilateral triangle = $$a$$ and side of regular hexagon = $$s$$

According to ques, => $$3a=6s$$

=> $$a=2s$$

Now, ratio of the area of the triangle to that of the hexagon :

= $$(\frac{\sqrt3}{4} a^2):(\frac{3\sqrt3}{2}s^2)$$

=> $$\frac{1}{2} (2s)^2=3s^2$$

=> $$2:3$$

=> Ans - (B)

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