Question

$\triangle ABC$ is an equilateral triangle of side $2a$. The length of each of its altitudes will be:

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

Hint:

In an equilateral triangle, altitude = median = $\frac{\sqrt{3}}{2}$ × side.

Answer 1

The Correct Option is C

Step 1: Formula for altitude of an equilateral triangle.
For a triangle of side $s$, altitude $h = \frac{\sqrt{3}}{2} s$.

Step 2: Substitute the given side.
\[ h = \frac{\sqrt{3}}{2} \times 2a = a\sqrt{3} \]
Step 3: Conclusion.
Hence, the length of each altitude is $a\sqrt{3}$.