Question
Determine whether these three side lengths will form a triangle: 6 cm, 8 cm, and 10 cm.(1 point)
Responses which is the true correct response
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 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 cannot form a triangle because the sum of any two of the side lengths is less than the length of the third side.
Responses which is the true correct response
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 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 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 whether the three side lengths (6 cm, 8 cm, and 10 cm) will form a triangle, we can apply the Triangle Inequality Theorem. This theorem states that for any three sides \( a \), \( b \), and \( c \) of a triangle, 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 sides 6 cm, 8 cm, and 10 cm:
1. \( 6 + 8 = 14 > 10 \) (True)
2. \( 6 + 10 = 16 > 8 \) (True)
3. \( 8 + 10 = 18 > 6 \) (True)
Since all three conditions are satisfied, these side lengths will form a triangle.
Therefore, 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 sides 6 cm, 8 cm, and 10 cm:
1. \( 6 + 8 = 14 > 10 \) (True)
2. \( 6 + 10 = 16 > 8 \) (True)
3. \( 8 + 10 = 18 > 6 \) (True)
Since all three conditions are satisfied, these side lengths will form a triangle.
Therefore, 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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