Let an equilateral triangle have the length of each side an integer $N$. I need to find if it is possible to transform the triangle keeping two sides fixed and alter the third side such that it still remains a triangle, but the altered side will have its length as an even integer, and the line drawn from the opposite vertex to the mid-point of the altered side is of integral length, i.e. it becomes an isosceles triangle.
Example : If $N=5$ then the answer is YES while if $N=3$ answer is NO.
It's a computer graphics problem that is a sub-part of bigger problem, I have been racking brains about maths and the concept behind it, to solve my problem.