Question 318405
{{{drawing(300,300,-10,10,-10,10,circle(-5,5,.3),circle(-5,-5,.3),circle(5,-5,.3),circle(5,5,.3),line(5,5,-5,-5),line(-5,5,5,-5),line(5,5,-5,5),line(-5,5,-5,-5),line(-5,-5,5,-5),line(5,-5,5,5),locate(5.9,0,s),locate(-6.2,0,s),locate(0,6.2,s),locate(0,-5.8,s),locate(2,4,d),locate(3,2,d),locate(-3,-1,d),locate(-2,-3,d),locate(-2,4,d),locate(-3,2,d),locate(2,-3,d),locate(3,-1,d))}}}
The perimeter of each triangle is,
{{{Pt=s+2d}}}
The total for 4 triangles would be,
{{{P=4s+8d}}}
{{{d}}} is related to the diagonal of the square,
{{{D=d+d=2d}}}
{{{D^2=s^2+s^2=2s^2}}}
{{{D=sqrt(2)*s}}}
Substituting,
{{{P=4s+8d}}}
{{{P=4s+4D}}}
{{{P=4(s+sqrt(2)s)}}}
{{{highlight(P=4s(1+sqrt(2)))}}}