The correct option is D at least one is irrational
Let the vertices of the equilateral triangle be (x1,y1),(x2,y2) and (x3,y3)
Area of an equilateral triangle =√34(side)2=irrational
Also, the area of triangle can be written as
If all the vertices of the triangle are rational, then Δ=rational
Both the statements are contradictory to each other. So at least one of the coordinates of the third vertex should be irrational.