Triangle inequality theorem-are the lengths 7, 4, and 2 of a triangle possible?

You can't make a triangle with those lengths for sides.

The way I look at it is like this:

-- Take  2  sticks ... lengths  4  and  2  ... and connect them together at one end.

-- The farthest they can reach, if they're opened up completely and pointing
in opposite directions, is a distance of  6 .

-- They can't reach the ends of a stick that is  7  long.  So you can't make
a triangle with those  3  sticks.