Find the perimeter of the square that has a diagonal of 32 centimeters. *no image included*

Ok so find the legnth of one side
if we drwa the diagonal, we cut the squre into 2 right triangles with legs equal measure

pythagorean theorem
for a right triangle with legs legnth a and b, and hypotnuse legnth c
a^2+b^2=c^2
since square, a=b
a^2+a^2=c^2
2a^2=c^2
diagonal=hypotnuse=32
2a^2=32^2
2a^2=1024
divide both sides by 2
a^2=512
sqrt both sides
a=16√2

the perimiter is 4 times one side
side=a=16√2
4 times 16√2=64√2

permiter is 64√2 cm