Question

The height of an equilateral triangle having each side 12 cm, is
(a) $6\sqrt{2}\mathrm{cm}$
(b) $6\sqrt{3}\mathrm{cm}$
(c) $3\sqrt{6}\mathrm{cm}$
(d) $6\sqrt{6}\mathrm{cm}$

Answer 1

(b) $6\sqrt{3}\mathrm{cm}$

Let ABC be the equilateral triangle with AD as its altitude from A.

In right-angled triangle ABD, we have:

$$\begin{gathered} A{B}^2=A{D}^2+B{D}^2 \\ A{D}^2=A{B}^2-B{D}^2 \\ ={12}^2-6^2 \\ =144-36=108 \\ AD=\sqrt{108}=6\sqrt{3}\mathrm{cm} \end{gathered}$$