Question 404446
diagonal  = d

apply pythagoras theorem

Let the legs be x each

..
d^2= x^+x^2
d^2=2x^2
divide by 2
d^2/2= x^2
{{{x= sqrt(d^2/2)}}}
{{{x=d/(sqrt(2))}}}

Perimeter = 4*length
{{{Perimeter = 4*d/(sqrt(2))}}}
{{{Perimeter = 2sqrt(2)*d}}}