Question

Find the height of equilateral triangle having side '2a'.

Answer 1

Given: An equilateral triangle having side=2a.

therefore, AB=BC=AC=2a. Draw AD perpendicular to BC such that BD=DC=a.

Now, from triangle ACD,

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

$(2a)^{2}=a^{2}+(AD)^{2}$

$4a^{2}-a^{2}=(AD)^{2}$

$AD=\sqrt{3}a$

$Therefore, \: height \: of \: an \: equilateral \: triangle \: is \: AD=\sqrt{3}a$