Answer:
The measures that would NOT produce a triangle are:
- three sides: 5 cm, 9 cm, and 15 cm
- three sides: 3 cm, 5 cm, and 10 cm
Step-by-step explanation:
To determine which measures would NOT produce a triangle, we need to consider the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's analyze each set of measures:
1. three sides: 3 cm, 5 cm, and 7 cm
- In this case, the sum of the two shorter sides (3 cm + 5 cm) is 8 cm, which is greater than the length of the longest side (7 cm). Therefore, a triangle can be formed with these measures.
2. three sides: 5 cm, 7 cm, and 9 cm
- Again, the sum of the two shorter sides (5 cm + 7 cm) is 12 cm, which is greater than the length of the longest side (9 cm). Hence, a triangle can be formed with these measures.
3. three sides: 5 cm, 9 cm, and 15 cm
- Here, the sum of the two shorter sides (5 cm + 9 cm) is 14 cm, which is less than the length of the longest side (15 cm). According to the triangle inequality theorem, a triangle cannot be formed with these measures.
4. three sides: 3 cm, 5 cm, and 10 cm
- Similarly, the sum of the two shorter sides (3 cm + 5 cm) is 8 cm, which is less than the length of the longest side (10 cm). Therefore, a triangle cannot be formed with these measures either.
Based on the analysis, the measures that would NOT produce a triangle are:
- three sides: 5 cm, 9 cm, and 15 cm
- three sides: 3 cm, 5 cm, and 10 cm
Answer:
-----------
Step-by-step explanation:
The triangle side-length rule states that the sum of the lengths of any two sides must be greater than the length of the remaining side
5 9 15 will not be a triangle 5 + 9 is not > 15
3 5 10 will not be a triangle 3 + 5 is not > 10
