Question
Question
Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point)
Responses
They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
They will form a triangle because the sum of any two of the side lengths is less than the length of the third side.
They will form a triangle because the sum of any two of the side lengths is less than the length of the third side.
They cannot form a triangle because the sum of any two of the side lengths is less than the length of the third side.
Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point)
Responses
They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
They will form a triangle because the sum of any two of the side lengths is less than the length of the third side.
They will form a triangle because the sum of any two of the side lengths is less than the length of the third side.
They cannot form a triangle because the sum of any two of the side lengths is less than the length of the third side.
Answers
GPT-4o mini
To determine whether the side lengths of 6 cm, 8 cm, and 10 cm can form a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check the conditions:
1. 6 cm + 8 cm > 10 cm → 14 > 10 (True)
2. 6 cm + 10 cm > 8 cm → 16 > 8 (True)
3. 8 cm + 10 cm > 6 cm → 18 > 6 (True)
Since all three conditions are satisfied, the three side lengths can indeed form a triangle.
The correct response is:
**They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.**
Let's check the conditions:
1. 6 cm + 8 cm > 10 cm → 14 > 10 (True)
2. 6 cm + 10 cm > 8 cm → 16 > 8 (True)
3. 8 cm + 10 cm > 6 cm → 18 > 6 (True)
Since all three conditions are satisfied, the three side lengths can indeed form a triangle.
The correct response is:
**They will form a triangle because the sum of any two of the side lengths is greater than the length of the third side.**