In an equilateral triangle, each side is ‘a’ units. The altitude of this triangle is:

Correct option is A

Given:

Side of the equilateral triangle = a

Solution:

In equilateral triangle ABC with side a , if we draw an perpendicular from the point A it divides the side BC at D into two equal halves such that BD = DC.

Then in right angled triangle ADC, altitude AD is Height , AC is hypotenuse and DC is base

Such that, 

​$$AC^2 = AD^2 + DC^2$$​​

​$$a^2 = AD^2 + (\frac{a}{2})^2$$​​

​$$AD^2 = a^2 - \frac{a^2}{4}$$​​

​$$AD^2 = \frac{3a^2}{4}$$​​

​$$AD = \frac{a\sqrt{3}}{2}$$ 

The altitude of equilateral triangle is $$\frac{\sqrt{3}\ a}{2}$$ cm