Perimeter of a triangle

Question

A question states:

The length of each side of a certain triangle is an even number.If no two sides have the same length what is the smallest perimeter the triangle could have ?

According to the author the answer is 18 but i think the answer is 12. (Scalene triangle with 2+4+6 as sides). Any suggestions please?

Answer 1

The sum of the lengths of any two sides of a triangle must be greater than the third side.

Answer 2

Your "triangle" looks like this:

2+4=6, so the long side coincides with the other two.

Answer 3

The lengths of 2, 4, and 6 as sides imply a trivial triangle with vertices on one line:

remember the triangle inequality $\|x + y\| \le \|x\| + \|y\|$ with equality only if $x,y$ are linearly dependent.