Answer:
Question 9: True
Question 10: False
Step-by-step explanation:
The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the last side.
To test if the three lengths create a triangle you would have to test the three combinations if the two numbers are greater than the last number.
Question 9:
The three lengths 6, 6, 5 create a triangle.
First check the first two numbers.
- 6 + 6 = 12
- 12 > 5, so this is valid.
Next check the first and last number.
- 6 + 5 = 11
- 11 > 6, this is also valid.
Last check the second and last number.
- 6 + 5 = 11
- 11 > 6, all three combinations are valid for creating a triangle.
The answer for question 9 is TRUE.
Question 10:
The three lengths 7, 2, 5 create a triangle.
Check the first two numbers.
- 7 + 2 = 9
- 9 > 5, this is valid.
Check the first and last number.
- 7 + 5 = 12
- 12 > 2, this is also valid.
Finally, check the second and last number.
- 2 + 5 = 7
- 7 = 7, this is NOT valid because it MUST be greater than. Therefore these three lengths are not able to create a triangle.
The answer for question 10 is FALSE.
