Question
Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point)
Responses
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 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 less 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 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.
Responses
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 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 less 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 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.
Answers
GPT-4o mini
To determine whether the side lengths 6 cm, 8 cm, and 10 cm can form a triangle, we can use the triangle inequality theorem. According to this theorem, for any three side lengths \(a\), \(b\), and \(c\), the following conditions must be met:
1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)
Let's check these conditions for the given side lengths:
1. \(6 + 8 = 14 > 10\) (True)
2. \(6 + 10 = 16 > 8\) (True)
3. \(8 + 10 = 18 > 6\) (True)
Since all three conditions are satisfied, the side lengths will form a triangle.
Thus, 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.**
1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)
Let's check these conditions for the given side lengths:
1. \(6 + 8 = 14 > 10\) (True)
2. \(6 + 10 = 16 > 8\) (True)
3. \(8 + 10 = 18 > 6\) (True)
Since all three conditions are satisfied, the side lengths will form a triangle.
Thus, 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.**