Question

The base of an equilateral triangle with side 2a lies along the y-axis such that the mid point of the base is at origin. Find the vertices of the triangle.

Answer 1

Length of side of equilateral triangle = 2a.

The base of triangle lies along y-axis and the mid point of base is at origin so that the co-ordinates of vertices are (0, a) and (0, - a).

Let vertices of the third vertex be ($\pm$ x, 0).

Then $\frac{1}{2}\times 2a\times (\pm x)=\frac{\sqrt{3}}{4}\times (2a{)}^2$

$\Rightarrow x=\pm \sqrt{3}a$

So the vertices of triangle are (0, a), (0, - a) and $(\sqrt{3}a,0)$ and (0, a), (0, -a) and $(-\sqrt{3}a,0)$.