SOLUTION: If the circumference of a circle is 20 centimeters, what is the perimeter of the square?

We can't tell whether the square is inscribed in or circumscribed
about the circle.

That is, we can't tell which of these you mean:

   

In either case we draw a diameter of the circle (in green)

   

In either case we find the diameter using the formula

C = pd

20 = pd

 = d

So the diameter of the circle in either case is  cm

   

In the first case, the green line is a diagonal of the square and
forms two isosceles right traingles.  So the two side are equal,
say x,



By the Pythagorean theorem,

x² + x² = 

    2x² = 

Divide both sides by 2

     x² = 

Take positive square roots of poth sides

      x = 

      x = 

      x = 

      x = 

Divide top and bottom by 2

      x = 

Since it has 4 sides, the perimeter

is  cm

or  cm

In the second case each of the four sides of the
square equals the diameter of the circle. So the 
primeter is  or  cm.  

Edwin