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 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.
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 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 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.
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 less than the length of the third side.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine if the side lengths 6 cm, 8 cm, and 10 cm can form a triangle, we can use the triangle inequality theorem. The theorem states that for any triangle with sides \( a \), \( b \), and \( c \):
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)
Let's check the three inequalities with 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 6 cm, 8 cm, and 10 cm **will 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.**
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)
Let's check the three inequalities with 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 6 cm, 8 cm, and 10 cm **will 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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