Question

semi new user here, would like some help with the following.

how would I go about listing "all" the side lengths of a triangle if i am given a perimeter of 15?

Answer 1

You need more information.
Are you told the sides are all congruent?
Are you told the side lengths are whole numbers?
Are you told some relationship between the side lengths?

Answer 2

no, all i am told is to the list the all the possible triangle. i have an equilateral triangle.

5+5+5 =15

i dont know how i would show anything else.

Answer 3

triangle side lengths*

Answer 4

there is a theorem to do with triangles stating that the sum of any 2 pairs of sides has to be equal to or greater than the third side, can this help you?

Answer 5

i am not given any sides, just perimeter.

Answer 6

sorry, just greater to , not equal (it's the triangle inequality)

Answer 7

you can use that information to set up a system of equations like a+b>c, b+c>a, and a+c>b, then solve it somehow? other thatn that, im out of ideas

Answer 8

yea. same here. im just going to with equilateral triangle.

Answer 9

thanks!!

Answer 10

If it's an equilateral triangle with perimeter 15, then all sides measure 5.

Answer 11

yes, but is there any other sides i can get with a perimeter of 15? and how ?

Answer 12

There is an infinite number of lengths of sides that will give you 15 perimeter.
Are the numbers all whole numbers? That will limit the total number choices.

Answer 13

ill just do it and show you how, so the perimeter is 15, that means the equalateral triangle has sides of length 5, so one is x=5, y=5, z=5
now x+y>z
x+z>y
and z+y>x
that means that no side can be over the halfway point of 15 which rounded down in this case is 7, that means that x<=7,y<=7,z<=7
does that help you? if not, ill finish the problem

Answer 14

yes they do have to be whole numbers, sorry should have stated this more clearly.

Answer 15

can you finish the problem, just so i grasp what you're trying to explain.

Answer 16

ok, so we have our 3 restrictions on the problem, x<=7,y<=7, and z<=7 and none of the values can be 0.
then it's just a combination of numbers (if x=1, then y can equal 7 and z can equal 6, or vice versa, etc...), you can repeat the whole process until you get to x=7

Answer 17

hmmm...