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