Integral Equilateral Triangle

Level 1

If the vertices of a triangle of a triangle have integral coordinates, then can the triangle be equilateral?

Sometimes No Not enough information Yes

1 solution

Maria Kozlowska
Oct 20, 2017

Area of any triangle with integral coordinates can be expressed as $\dfrac{n}{2}$ , for some positive integer $n$ . Area of equilateral triangle is

$\dfrac{\sqrt{3}}{4} a^2$

where $a$ is triangle side length. $a^2$ is always an integer, so the area can not have a rational value. Therefore the answer is no.