"the diagonal splits the square into 2 congruent right angled"the diagonal splits the square into 2 congruent right angled
"triangles"triangles
"choosing 1 right triangle and applying "color(blue)"Pythagoras' theorem"choosing 1 right triangle and applying Pythagoras' theorem
"let the side of the square "=xlet the side of the square =x
"the diagonal is the hypotenuse of the triangle"the diagonal is the hypotenuse of the triangle
rArrx^2+x^2=6^2 larrcolor(blue)" Pythagoras' theorem"⇒x2+x2=62← Pythagoras' theorem
rArr2x^2=36⇒2x2=36
"divide both sides by 2"divide both sides by 2
rArrx^2=18⇒x2=18
color(blue)"take the square root of both sides"take the square root of both sides
rArrx=+-sqrt18 larr" length must be positive"⇒x=±√18← length must be positive
rArrx=sqrt18=sqrt9xxsqrt2=3sqrt2⇒x=√18=√9×√2=3√2