Question

find the hight of an equilateral triangle having side 2a​

Answer 1

Answer:

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}(AC)

2

=(AD)

2

+(DC)

2

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

2

=a

2

+(AD)

2

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

2

−a

2

=(AD)

2

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

2

=(AD)

2

AD=\sqrt{3}aAD=

3

a

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

3

a