Question 990493
For a square,
{{{A[s]=s^2}}}
{{{P[s]=4s}}}
For a equilateral triangle,
{{{A[et]=(sqrt(3)/4))x^2}}}
{{{P[et]=3x}}}
So {{{A[s]=A[et]}}}
{{{s^2=(sqrt(3)/4)x^2}}}
{{{s^2/x^2=sqrt(3)/4}}}
{{{(s/x)=sqrt(sqrt(3)/4)}}}
{{{(s/x)=3^(1/4)/2}}}
And,
{{{P[s]/P[et]=(4s)/(3x)=(4/3)(s/x)=(4/3)(3^(1/4)/2)=2/3^(3/4)}}}