Question

Calculate the height of an equilateral triangle each of whose sides measures $12cm$.

Answer 1

The altitude of an equilateral triangle bisects the side on which it stands and forms right-angled triangles with the remaining sides.

So, $CD=DB=6cm$

Also in $△ADC,\angle ADC={90}^{\circ }$

Applying Pythagoras theorem gives

$(AC{)}^2=(CD{)}^2+(AD{)}^2$

$(12{)}^2=(6{)}^2+(AD{)}^2$

$144=36+(AD{)}^2$

$(AD{)}^2=108$

$AD=\sqrt{108}=6\sqrt{3}cm$

The height of equilateral triangle $=6\sqrt{3}cm$