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Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
Responses:
12, 10, 22
9, 4, 3
8, 1, 7
2, 7, 6
Bot GPT 3.5
answered
To determine if a set of side measures will form a triangle, we need to apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each group of side measures:
1) 12, 10, 22
To form a triangle, the sum of any two sides must be greater than the length of the third side. However, 12 + 10 = 22, which is equal to the length of the third side. This means that these side measures will NOT form a triangle.
2) 9, 4, 3
In this case, the smallest side length is 3. To form a triangle, the sum of the other two sides must be greater than 3. However, 9 + 4 = 13, which is greater than 3. Additionally, 9 + 3 = 12, and 4 + 3 = 7, both of which are also greater than 3. Therefore, these side measures WILL form a triangle.
3) 8, 1, 7
Once again, the smallest side length is 1. Adding the other two side lengths, we get 8 + 7 = 15, which is greater than 1. The sum of the other two side lengths, 8 + 1, is also greater than 7, as well as 1 + 7 being greater than 8. Hence, these side measures WILL form a triangle.
4) 2, 7, 6
The smallest side length is 2. The sum of the other two side lengths is 7 + 6 = 13, which is greater than 2. Additionally, 2 + 7 = 9, and 2 + 6 = 8, both of which are greater than 6. Therefore, these side measures WILL form a triangle.
In conclusion, the groups of side measures that will form a triangle are:
- 9, 4, 3
- 8, 1, 7
- 2, 7, 6
Traveler
answered
its only 1 answer, its not 9, 4, 3
Bot GPT 3.5
answered
I apologize for the error. You are correct. According to the Triangle Inequality Theorem, a set of side measures will only form a triangle if the sum of the lengths of any two sides is greater than the length of the third side.
Let's reevaluate the groups of side measures:
1) 12, 10, 22
To form a triangle, the sum of any two sides must be greater than the length of the third side. However, in this case, 12 + 10 = 22, which is equal to the length of the third side. Therefore, these side measures will NOT form a triangle.
2) 9, 4, 3
The sum of the two smallest side lengths, 4 + 3, is equal to 7, which is greater than the length of the largest side, 9. Similarly, the sum of the two larger side lengths, 9 + 4, is equal to 13, which is greater than the length of the remaining side, 3. Therefore, these side measures WILL form a triangle.
3) 8, 1, 7
In this case, the sum of the two smaller side lengths, 1 + 7, is equal to 8, which is greater than the length of the largest side, 8. Similarly, the sum of the two larger side lengths, 8 + 7, is equal to 15, which is greater than the length of the remaining side, 1. Therefore, these side measures WILL form a triangle.
4) 2, 7, 6
The sum of the two smaller side lengths, 2 + 6, is equal to 8, which is greater than the length of the largest side, 7. Similarly, the sum of the two larger side lengths, 7 + 6, is equal to 13, which is greater than the length of the remaining side, 2. Therefore, these side measures WILL form a triangle.
In conclusion, the group of side measures that will form a triangle is:
- 9, 4, 3