If the perimeter of a square measures 32 cm, each side measures 32/4= 8 cm, because all sides are equal.
The diagonal that passes through the center of the square divides the square into two triangles. The triangles are formed by a hypotenuse (the diagonal, which is k in this case), and two sides, that measure 8 cm each, in this case.
Because of Pythagoras' theorem, we know that the lenght of the hypotenuse (in this case the hypotenuse is k) equals the squared root of the sum of the squared sides, which in this case can be expressed as [tex]k=\sqrt{8^2+8^2} =\sqrt{64+64}=\sqrt{128}=11.31[/tex].
