Question

Find the coordinates of the vertices of an equilateral triangle of side 2a as shown in the figure.

Answer 1

REF.Image

Area = $\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}(2a{)}^2=\frac{\sqrt{3}}{4}\times 4a^2=\sqrt{3a^2}$

Area = $\frac{1}{2}\times b\times h$

$\sqrt{3}{a}^2=\frac{2a\times h}{2}$

$\therefore \sqrt{3}{a}^2=a\times h$

$\therefore h=\sqrt{3}a$

$\therefore$ The coordinates of the vertices

of an equilateral triangle are $\Rightarrow 0\equiv (0,0),A(2a,0)$ and $B(a,\sqrt{3}a)$