A square has a diagonal with the length of 6 meters, how do you find the lengths of the sides of the square?
1 Answer
Aug 1, 2017
Explanation:
#"the diagonal splits the square into 2 congruent right angled"#
#"triangles"#
#"choosing 1 right triangle and applying "color(blue)"Pythagoras' theorem"#
#"let the side of the square "=x#
#"the diagonal is the hypotenuse of the triangle"#
#rArrx^2+x^2=6^2 larrcolor(blue)" Pythagoras' theorem"#
#rArr2x^2=36#
#"divide both sides by 2"#
#rArrx^2=18#
#color(blue)"take the square root of both sides"#
#rArrx=+-sqrt18 larr" length must be positive"#
#rArrx=sqrt18=sqrt9xxsqrt2=3sqrt2#
