Question

find the height of an equilateral triangle having side 2a

Answer 1

=(underoot 3 )a
will be the height of that equilateral triangle..
by using pythagorus theorm
(hypotenuse )^2-(base)^2=(height)^2

Answer 2

Answer:

Step-by-step explanation:

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,

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

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

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

$3a^{2}=(AD)^{2}$

$AD=\sqrt{3}a$

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