Length of a Triangle's Sides
Date: 23 Jan 1995 14:05:32 -0500 From: Scott Rappard Subject: Braemore School Antigonish N.S. Canada Dear Dr. Math, My name is Matthew Rappard and I have a problem for you to solve. The lengths of the three sides of a triangle could be A 0,1,2 B 1,2,3 C 2,3,4 D 2,4,6 I got this problem from my teacher. My class could not get it, and the teacher can't get it either. We know the answer is C, but why? Thanks for your help Matthew Rappard
Date: 24 Jan 1995 01:11:21 GMT From: Dr. Math Subject: Re: Braemore School Antigonish N.S. Canada Hello there! Well, C is indeed the right answer. Think about the following property of triangles: A /\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ ____________________________________ B C Look at the distance between B and C. How far is it? You can measure if you want. That's the minimum possible distance along any path from B to C. Now what would happen if you had walked along a different path from B to C, like starting at B, walking to A, and then walking to C? It would be a longer trip, right? So what we've said is that the distance from B to C is less than the distance from B to A plus the distance from A to C. Or in equation notation, BC < BA + AC. You'll also notice that there was nothing special about BC, the same thing happens with AB or AC, and we have the following relations: BC < BA + AC (this is from before) BA < BC + AC AC < BC + BA These are the three relations that govern the sides of a triangle: if you add the lengths of any two sides, you'll get something bigger than the length of the third side. Now look at your possibilities for sides, and see whether you can figure out why they chose them like they did. Write back if you have more questions! -Ken "Dr." Math
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