Question

Find the length of the altitude of an equilateral triangle, each side measuring ${}^{\prime }{a}^{\prime }$ units.

• A. $\frac{\sqrt{3}}{2}a$
• B. $\frac{a}{2}$
• C. $\frac{\sqrt{2}}{3}a$
• D. $a$

Answer 1

The correct option is A $\frac{\sqrt{3}}{2}a$

We know that the measure of each angle of an equilateral triangle is ${60}^o$.

When an altitude is dropped from one vertex to the opposite side of the equilateral triangle, it becomes its perpendicular bisector.

Therefore, the equilateral triangle now gets divided into two triangles of measure ${30}^o,{60}^o,{90}^o$, each.

Using $30,60,90$ theorem we get,

$\therefore \text{altitude}=\frac{\sqrt{3}}{2}\times \text{side}$

Hence, option A is correct.