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Two triangles are considered the same if they have the same three side lengths. Find all possible values of P such that there is only 1 possible triangle with integer side lengths and perimeter P.

 Apr 22, 2021
 #1
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3
4

5

6

 Apr 22, 2021
 #2
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explain please?

Guest Apr 22, 2021
 #3
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Sorry XD

 

for a triangle to be possible, we must have

 

a+b>c

b+c>a and

c+a>b

 

where a b and c are all real positive integer side lengths.

 

the smallest possible number is 3, because that evenly divides into 1,1, and 1.

similarly, we have 4, 1,1, and 2, because either way you end up with the same iscocolese triangle.

we have 5, which has to be 1,2,2, not 1,1,3, because 1+1 is not greater than 3.

then we have 6, which has to be 2,2,2,  because 1,2,3 and 1,1,4 does not work for the same reason as 5.

for any number above 6, it works beacuse there are different ways to arrange the side lengths. 

 

hope that helped :)

 Apr 22, 2021
 #4
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WAit so there are infinte solutions?

Guest Apr 22, 2021

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