Asked by Shimmer Bloom
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 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.
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.
Responses
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.
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.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine if three side lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that for any three sides \( a \), \( b \), and \( c \) (where the sides are ordered such that \( a \leq b \leq c \)), the following must hold:
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)
For the side lengths given: 6 cm, 8 cm, and 10 cm:
1. \( 6 + 8 = 14 \) which is greater than \( 10 \)
2. \( 6 + 10 = 16 \) which is greater than \( 8 \)
3. \( 8 + 10 = 18 \) which is greater than \( 6 \)
Since all three conditions are satisfied, the lengths 6 cm, 8 cm, and 10 cm 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.**
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)
For the side lengths given: 6 cm, 8 cm, and 10 cm:
1. \( 6 + 8 = 14 \) which is greater than \( 10 \)
2. \( 6 + 10 = 16 \) which is greater than \( 8 \)
3. \( 8 + 10 = 18 \) which is greater than \( 6 \)
Since all three conditions are satisfied, the lengths 6 cm, 8 cm, and 10 cm 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.**
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.