State whether the statements are true or false.
If the vertices of a triangle have integral coordinates, then the triangle can’t be equilateral.
Let ABC be a triangle with vertices A(x1,y1), B (x2,y2) and C (x3, y3) where xi, yi, i=1,2,3 are integers
Then area of
Since, xi and yi all are integers but is a rational number.
So, the result comes out to be a rational number. i.e . Area of ABC=a rational number
Suppose, ABC be an equilateral triangle, then area of ABC is=
It is given that vertices are integral coordinates, it means the value of coordinates is in whole
number. Therefore, the value of (AB)2 is also an integer.
(positive integer)
But, is an irrational number
Area of triangle ABC=an ir-rational number
This contradicts the fact that the area is a rational number
Hence, the given statement is true.