Question

Given two side lengths of a triangle (4cm and 17cm), find a range of possible lengths for the third side.

Answer 1

Check the picture below.

so notice the top part of the picture

if we move the "4" and "17" sides  close to each other, till one is on top of the other, the side in red, can never be less than 17 - 4, or 13, it cannot be 13 either, because then both lines will be on on top and we wouldn't have a triangle just a flat-line, so whatever the red line is, it must be more than 13.

notice the bottom part of the picture

if we separate the "4" and "17" sides, and lay them flat, the most the red side can be is 4 + 17 or 21, it can never be greater than 21, it can't be 21 either because if we lay "4" and "17" flat, we lose the triangle and all we'd have is a flat-line.  So whatever the red side is, must be less than 21.