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

### 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

### 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

(9827-A)

I think the answers is 7,7 and 6

(9827-A)