<p>Okay let's say there's a triangle with 2 sides, lengths are (5 in./12 in.)... or another with sides (7 in., 1 in.).. Is there a rule for the longest and shortest the 3rd side can get?</p>
<p>the longest is the sum of the 2 other sides (17 and 8 in your examples), and the shortest is the difference (7 and 6).</p>
<p>wow… surprised i didn’t know that… but thank you very much good to know!</p>
<p>The 3rd side is actually STRICTLY between the difference and sum of the other two sides. The two extreme cases form lines, NOT triangles. </p>
<p>For example, if a triangle has sides of length 5, 12, and x, then 7 < x < 17. So there is NO longest or shortest length that x can be to form a triangle. If x = 7 or 17, then you get a line, NOT a triangle.</p>
<p>If the lengths MUST be integer lengths, then the shortest and longest lengths for x are 8 and 16, respectively. If the question asks about distances instead of specifically mentioning triangles, then the extreme cases of 7 and 17 are ok.</p>
<p>I was just thinking about that Dr. Steve… Picturing triangles in my head… Thank you for clarifying! I understand now :)</p>