Question

The Height Of An Equilateral Triangle Of Side $a$ Is Given By:

• A. $\frac{a\sqrt{2}}{2}$
• B. $\frac{a\sqrt{2}}{3}$
• C. $\frac{a\sqrt{3}}{2}$
• D. $\frac{a\sqrt{3}}{4}$

Answer 1

The correct option is C

$\frac{a\sqrt{3}}{2}$

Height Of An Equilateral Triangle

$$\begin{gathered} AreaofTriangle=\frac{1}{2}\times base\times height \\ Areaofequilateraltriangle=\frac{\sqrt{3}}{4}{a}^2 \\ \frac{1}{2}\times base\times height=\frac{\sqrt{3}}{4}{a}^2 \\ \frac{1}{2}\times a\times height=\frac{\sqrt{3}}{4}{a}^2 \\ height=\frac{a\sqrt{3}}{2} \end{gathered}$$

Hence, Option (C) is the correct answer.