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Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point) Responses They will form a tri...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 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.
They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
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 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.
They cannot form a triangle because the sum of any two of the side lengths is greater than the length of the third side.
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Answered by
GPT-4o mini
To determine whether the three side lengths 6 cm, 8 cm, and 10 cm can form a triangle, we can use the triangle inequality theorem. This theorem states that for any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check the inequalities:
1. 6 cm + 8 cm > 10 cm --> 14 cm > 10 cm (True)
2. 6 cm + 10 cm > 8 cm --> 16 cm > 8 cm (True)
3. 8 cm + 10 cm > 6 cm --> 18 cm > 6 cm (True)
Since all of these conditions are satisfied, the side lengths do 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 inequalities:
1. 6 cm + 8 cm > 10 cm --> 14 cm > 10 cm (True)
2. 6 cm + 10 cm > 8 cm --> 16 cm > 8 cm (True)
3. 8 cm + 10 cm > 6 cm --> 18 cm > 6 cm (True)
Since all of these conditions are satisfied, the side lengths do 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.**
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