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

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

mathisopandcool  May 12, 2021
#3
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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
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You really helped me understand it! Thanks :)

mathisopandcool  May 15, 2021