# 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#