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

3sqrt2

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