Question

Question Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.(1 point) Responses 2 2 1 1 9 9 11
Answer
pick one
Answer
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 12, 10, 22 12, 10, 22 2, 7, 6 2, 7, 6 8, 1, 7 8, 1, 7 9, 4, 3
Answer
pick one
Answered by GPT 3.5
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For a triangle with sides measuring 4 and 6, the third side must satisfy the following condition:

4 + 6 > x
10 > x

Therefore, the possible options for the third side of the triangle are:
- 2
- 9
- 11

So, the correct responses are 2, 9, and 11.
Answered by GPT 3.5
The correct response is 9.
Answered by GPT 3.5
To determine which group 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 evaluate each set of side measures:

1. For the first set, 12, 10, 22:
12 + 10 > 22 (TRUE)
10 + 22 > 12 (TRUE)
12 + 22 > 10 (TRUE)
This set forms a triangle.

2. For the second set, 2, 7, 6:
2 + 7 > 6 (TRUE)
7 + 6 > 2 (TRUE)
2 + 6 > 7 (TRUE)
This set forms a triangle.

3. For the third set, 8, 1, 7:
8 + 1 > 7 (TRUE)
1 + 7 > 8 (TRUE)
8 + 7 > 1 (TRUE)
This set forms a triangle.

4. For the fourth set, 9, 4, 3:
9 + 4 > 3 (TRUE)
4 + 3 > 9 (FALSE)
9 + 3 > 4 (TRUE)
This set does not form a triangle because the sum of the lengths of two sides is not greater than the length of the third side.

Therefore, the group of side measures that will form a triangle is:
- 12, 10, 22
- 2, 7, 6
- 8, 1, 7

The answers are:
- 12, 10, 22
- 2, 7, 6
- 8, 1, 7
Answered by GPT 3.5
12, 10, 22