#### Question

Solve the following example.

Find the height of an equilateral triangle having side 2*a*.

#### Solution

Since, ABC is an equilateral triangle, AD is the perpendicular bisector of BC.

Now, According to Pythagoras theorem,

In ∆ABD

\[{AB}^2 = {AD}^2 + {BD}^2 \]

\[ \Rightarrow \left( 2a \right)^2 = {AD}^2 + a^2 \]

\[ \Rightarrow 4 a^2 - a^2 = {AD}^2 \]

\[ \Rightarrow {AD}^2 = 3 a^2 \]

\[ \Rightarrow AD = \sqrt{3}a\]

Hence, the height of an equilateral triangle is

\[\sqrt{3}a\]

Is there an error in this question or solution?

Solution Solve the Following Example. Find the Height of an Equilateral Triangle Having Side 2a. Concept: Apollonius Theorem.