Given: ABC is an equilateral triangle
∴ AB = AC = BC = 12cm
And let AD is an altitude on BC. Therefore, BD = 1/2 x BC = 6 cm
Now, In ∆ADB, using Pythagoras theorem, we have
(Perpendicular)2 + (Base)2 = (Hypotenuse)2
⇒ (AD)2 + (BD)2 = (AB)2
⇒ (AD)2 + (6)2 = (12)2
⇒ (AD)2 = 144 – 36
⇒ (AD)2 = 108
⇒ AD = √108
⇒ AD = 6√3
Hence, the height of an equilateral triangle is 6√3 cm
