Question

The perimeter of a equilateral triangle and regular hexagon are equal. Find out the ratio of their areas?'

Answer 1

answer is 2:3

perimeter of equilateral triangle=3*side of triange(s1)

perimeter of hexagon=6*side of hexagon(s2)

area of equilateral triangle A1=(sqrt(3)/4)*s1*s1 =>s1*s1=(4*A1)/sqrt(3)

area of hexagon A2=(3*sqrt(3)/2)*s2*s2 =>s2*s2= (2*A2)/(3*sqrt(3))

GIVEN:

3*s1=6*s2

squaring it we get

9*s1*s1=36*s2*s2;

substituting the values calculated through area in above equation

9*4*A1/sqrt(3) =36*2*A2/(3*sqrt(3))

==>A1/A2=2/3

2:3