Question 201641
(1) diagon  separates  a  square  into  2  equal  triangles.  legs = "s",,
diagonal  =d,,,,as  it  is  a  right  triangle(square  corner),,
use  pythagorous,,c^2 = a^2  +b^2,,,with  a = b =s,,,c=d,
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d^2 = s^2 +s^2 =2s^2,,,,d = sqrt 2 s^2 = s*sqrt2,,,,,
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or (2)  recognize  that  the  triangles  are ,,,45-45-90,  with  side  ratios,
1-1-sqrt2,,or  s-s-s*sqrt2,,,and  see  d= s*sqrt2