Question 1171698
<br>
Refer to picture below.<br>

From the Pythagorean Theorem, 

{{{ s^2 + s^2 = 10^2 }}}
{{{ 2s^2 = 100 }}}
{{{ s^2 = 50 }}}
{{{ s = sqrt(50) }}}cm  or about 7.07cm
<br>
NOTE that the side length of a square is related to its diagonal length
by  {{{sqrt(2)}}} :  diagonal_length = {{{sqrt(2)}}}* side_length.  Try
it out with a calculator, or better, derive it from the picture. 
<br>


{{{ drawing(400,400,-1,8,-1,8, grid(0),
     line(0,0,7,0),
     line(7,0,7,7),
     line(7,7,0,7),
     line(0,7,0,0),
     green(line(0,0,7,7)),
     locate(3.4,4.2,"10"),
     locate(7.3,4,"s"),
     locate(3.4,0.5,"s")

)
}}}