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

3sqrt232

Explanation:

"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=362x2=36

"divide both sides by 2"divide both sides by 2

rArrx^2=18x2=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=3sqrt2x=18=9×2=32