# If the vertices of a traingle have integral coordinates, prove that the triangle cannot be equilateral. Solve it and what is integral coordinates?

Dear Student,

Let us take the vertices of the triangle as , where all these coordinates are integers.

∴ Area of the triangle =

Since all the coordinates are integers, therefore, the area will be rational.

Let us assume that the triangle is equilateral, with length of its each side being s.

∴ Area of the triangle =

which is an irrational value.

Hence, our assumption that the area is rational, is wrong.

Thus, the triangle with integral coordinates can not be an equilateral triangle.

Integral coordinates are coordinates that are whole numbers. Integral coordinates cannot be fractional or have decimals.

Regards

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