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
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
9 answers
which one
The valid third side option is 9.
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
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
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
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
which one
All of the given options can form a triangle according to the Triangle Inequality Theorem.
pick the most reasonable one
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.
- 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.