Question

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

Answer 1

perimeter of a equilateral triangle =perimeter of regular hexagon =P
side of equilateral triangle =P/3
and of regular hexagon =P/6
area of eq. tr.=(rt 3)/4*(P/3)^2
area of regular hexagon=6*area of eq. tr.
=6*(rt 3)/4*(P/6)^2
ratio of areas=(P/3)^2/6*(P/6)^2
=(1/9)/(6*1/36)=(1/9)*6=2:3