Question

Can the numbers 12,6 , 6 be used to form the sides of a triangle

Answer 1

we have three sides, let's look at the two smaller sides first.

check the picture below, atop

if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side?  Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 6 - 6 = 0.  However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle.  So whatever the third side may be, it must be greater than 0.

check the picture below, at the bottom

Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 6 + 6 = 12.  However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle.  So whatever the third side may be, it must be less than 12.

so, 12 is  a no dice.