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How many non congruent triangles with positive integer side lengths have perimeter less than 18?

 May 22, 2021
 #1
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In attempting to list them, I got

8 triangles with smallest side = 1

11 triangles with smallest side = 2

13 triangles with smallest side = 3

10 triangles with smallest side = 4

4 triangles with smallest sides = 5

 May 23, 2021
 #2
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we have to find how many non congruent triangles with positive integer side lengths have perimeter less than 18.

 

we have non congruent triangles with positive integer side lengths have perimeter less than 18 as 

8+11+13+10+4=46 triangles.

8 triangles having smallest side = 1 unit

11 triangles having smallest side = 2 unit

13 triangles having smallest side = 3 unit

10 triangles having smallest side = 4 unit

4 triangles having smallest sides = 5 unit.

 May 23, 2021

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