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

9
9

11
11

1

Answer 1

which one

Answer 2

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

8, 1, 7
8, 1, 7

2, 7, 6
2, 7, 6

9, 4, 3
9, 4, 3

Answer 3

which one

Answer 4

pick the most reasonable one

Answer 5

To apply the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the first two sides measure 4 and 6.

Let's determine if the third side length options satisfy the triangle inequality theorem:

1) 2: 4 + 2 = 6 (greater than 2), 2 + 6 = 8 (greater than 4), 2 + 4 = 6 (equal to 6) - Not valid.

2) 9: 4 + 9 = 13 (greater than 6), 6 + 9 = 15 (greater than 4), 9 + 4 = 13 (greater than 6) - Valid.

3) 11: 4 + 11 = 15 (greater than 6), 6 + 11 = 17 (greater than 4), 11 + 4 = 15 (greater than 6) - Valid.

1 is not a valid option as it does not satisfy the triangle inequality theorem.

Therefore, the valid third side options are:

- 9
- 11

Answer 6

The valid third side option is 9.

Answer 7

To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let's check each group of side measures:

1) 12, 10, 22:
12 + 10 = 22 (equal to 22, but it should be greater), 10 + 22 = 32 (greater than 12), 12 + 22 = 34 (greater than 10)
This group of side measures does not satisfy the Triangle Inequality Theorem.

2) 8, 1, 7:
8 + 1 = 9 (greater than 7), 1 + 7 = 8 (greater than 8), 8 + 7 = 15 (greater than 1)
This group of side measures satisfies the Triangle Inequality Theorem.

3) 2, 7, 6:
2 + 7 = 9 (greater than 6), 7 + 6 = 13 (greater than 2), 2 + 6 = 8 (greater than 7)
This group of side measures satisfies the Triangle Inequality Theorem.

4) 9, 4, 3:
9 + 4 = 13 (greater than 3), 4 + 3 = 7 (greater than 9), 9 + 3 = 12 (greater than 4)
This group of side measures satisfies the Triangle Inequality Theorem.

From these options, the group of side measures that will form a triangle is:
- 8, 1, 7
- 2, 7, 6
- 9, 4, 3

Answer 8

All of the given options can form a triangle according to the Triangle Inequality Theorem.

Answer 9

Based on the given options, the most reasonable group of side measures that forms a triangle is:

- 9, 4, 3

This is because the sum of the lengths of any two sides of the triangle is greater than the length of the third side:

9 + 4 = 13 (greater than 3)

4 + 3 = 7 (greater than 9)

9 + 3 = 12 (greater than 4)

Therefore, the most reasonable option that forms a triangle is 9, 4, 3.