Directions: The perimeter of a triangle is 20 units. Using whole numbers, how many sets of side lengths can you find for this triangle?

### Hint

Can one of the side lengths be 10? Why or why not?

Can one of the side lengths be 20? or more than 20? Why or why not?

What is true about the sum of any two sides of a triangle compared to the third side?

Is a triangle with the sides 3, 4, 5 different than a triangle with the sides 4, 5, 3? Does the order matter?

Can one of the side lengths be 20? or more than 20? Why or why not?

What is true about the sum of any two sides of a triangle compared to the third side?

Is a triangle with the sides 3, 4, 5 different than a triangle with the sides 4, 5, 3? Does the order matter?

### Answer

2, 9, 9

3, 8, 9

4, 7, 9

5, 6, 9

6, 6, 8

7, 7, 6

8, 8, 4

3, 8, 9

4, 7, 9

5, 6, 9

6, 6, 8

7, 7, 6

8, 8, 4

These are the whole number sets of side lengths my students found. There may be more.

Source: Christina Ploeckelman

5, 7, 8

I think I know how you came up with the answers.

I think I know too!

I think there are 7 sets of side lengths that could make up the perimeter of 20 units on a triangle

7, 7, and 6

I think the answers is 7,7 and 6

(9827-A)

I think the answer is 6, 6, 8

‘does the order matter.” Yes the order does matter because 4,7,9 don’t make a triangle and niether does 8,8,4 i double checked and it never came out right there for they have to be wrong.Also i tested out the rest and they seemed to work it was those two that caught my eye and came out incorrect.

the issue I have here is this is a great question… but can’t the student just google it? And find the answer here? If I am teaching virtually, I am not able to prevent this. So can you provide other possible values to use without the answers? Thanks

Just change the perimeter from 20 to 30. That should stump most students who try to google.

I think the answer is 7,7,6 because the two sides of a triangle are longer than the bottom.