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How many non-congruent triangles with perimeter 15 inches are there whose side lengths are all integer numbers of inches?

 May 12, 2021
 #1
avatar+1940 
0

5, 5, 5, 

4, 5, 6

3, 6, 6

4, 4, 7

3, 5, 7

2, 6, 7

1, 7, 7

7 options :)

=^._.^=

 May 12, 2021
 #2
avatar+199 
0

thxs:) is there any other way to solve it other than just finding all the possible combinations?

mathisopandcool  May 12, 2021
 #3
avatar+1940 
0

Absolutely, but I think this way might just be the best way for small cases like this. 

It is actually quite efficient if you have a system. 

15/3 = 5

15/2 = 7.5

So the highest number has to be 5-7. 

5: 1 option 

6: 2 options

7: 4 options

 

You could also use complementary counting, find all numbers that add up to 15, then subtract the ones that don't work for a triangle. :))

=^._.^=

catmg  May 12, 2021
 #4
avatar+199 
0

You really helped me understand it! Thanks :)

mathisopandcool  May 15, 2021

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