Q48 of 59 Page 178

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 (x2, y2), where xi, yi, i = 1, 2, 3 are integers

Then, Area of ΔABC



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 ΔABC = a rational number


Suppose, ABC be an equilateral triangle, then Area of ΔABC is



[∵ AB = BC = CA]


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.



But, √3 is an irrational number.


⇒ Area of ΔABC = an ir-rational number


This is a contradiction to the fact that the area is a rational number.


Hence, the given statement is TRUE


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