Question

If two sides of a triangle have lengths 4 and 9 then the length of the third side may be any number

Answer 1

check the picture below.

on the first case, in green, if we lay the 4 side down flat on top of the 9 side, the lenght of "x" will be 9 - 4, or 5, however, we can't do that, because if we do, we end up with a flat-line and lose the triangle, so "x" can't be smaller than 5, it has to be larger than 5.

on the second case, if we lay the 4 side the other way flat on the ground, "x" will be of length 4 + 9, or 13, however, again, we can't do that, because if we do we'd lose our triangle again, so "x" can't be larger than 13, it has to be smaller than 13.