Question

A square has a diagonal with the length of 6 meters, how do you find the lengths of the sides of the square?

Answer 1

`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`