Question

$ABC$ is an equilateral triangle of side $2a$. Find each of its altitudes.

• A. $a\sqrt{3}$
• B. $2a\sqrt{3}$
• C. $a\sqrt{2}$
• D. $a\sqrt{6}$

Answer 1

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

Area of a triangle = $\frac{1}{2}base\times height$
Area of equilateral triangle = $\frac{\sqrt{3}}{4}{s}^2$
Equating,
$\frac{\sqrt{3}}{4}(2a{)}^2=\frac{1}{2}(2a\left)\right(height)$
$\sqrt{3}{a}^2=a\left(height\right)$
$height=a\sqrt{3}$