All the sides of a triangle are integers, and the perimeter is 15. How many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are congruent.)

Guest Mar 12, 2021

#1**+1 **

we can say that one side length is a, another b, and the last c. We know that:

a+b>c

a+c>b

c+b>a

a+b+c=15

We also know that order matters. if a=1, b and c must be 7. if a=2, b must be 7, and c must be 6. we can continue counting:

a=1,b=7,c=7

a=2,b=7,c=6

a=3,b=6,c=6

a=3,b=7,c=5

a=4,b=6,c=5

a=4,b=7,c=4

a=5,b=5,c=5

those are all the possible solutions, so $\boxed{7}$ is our answer

SparklingWater2 Mar 12, 2021

#1**+1 **

Best Answer

we can say that one side length is a, another b, and the last c. We know that:

a+b>c

a+c>b

c+b>a

a+b+c=15

We also know that order matters. if a=1, b and c must be 7. if a=2, b must be 7, and c must be 6. we can continue counting:

a=1,b=7,c=7

a=2,b=7,c=6

a=3,b=6,c=6

a=3,b=7,c=5

a=4,b=6,c=5

a=4,b=7,c=4

a=5,b=5,c=5

those are all the possible solutions, so $\boxed{7}$ is our answer

SparklingWater2 Mar 12, 2021