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All the sides of a triangle are integers.  If the perimeter of the triangle is $5,$ then how many different possible triangles are there?  (Assume that the triangle is non-degenerate.  Two triangles are considered the same if they are congruent.)

 Jun 8, 2024
 #1
avatar+806 
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There's actually only one triangle that satisfies all the rules stated.

 

The only one that works is 

 

2-2-1

 

Any other triangle would violate the triangle inequality theorems, therefore being invalid. 

 

So 1 is our answer!

 

Thanks! :)

 Jun 8, 2024

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