Question

$\Delta ABC$ is an equilateral triangle of side 2a units. Find each of its altitudes.

Answer 1

Let AD be the altitude in equilateral triangle ABC.

In an equilateral triangle, the altitude cuts the side into two equal parts. Since BC =2a, BD=DC=a

From Pythagoras theorem,

$A{D}^2=A{C}^2-D{C}^2=(2a{)}^2-a^2=4a^2-a^2=3a^2$

$AD=\sqrt{3}a$

So, each altitude is equal to $\sqrt{3}a$