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 9 9 2 2 1 1 11

Answer 1

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

In this case, the first two sides measure 4 and 6. Let's check each option:

1. 9: 4 + 6 = 10 > 9. This option satisfies the Triangle Inequality Theorem.
2. 9: 4 + 6 = 10 > 9. This option satisfies the Triangle Inequality Theorem.
3. 2: 4 + 6 = 10 < 2. This option does not satisfy the Triangle Inequality Theorem.
4. 2: 4 + 6 = 10 < 2. This option does not satisfy the Triangle Inequality Theorem.
5. 1: 4 + 6 = 10 < 1. This option does not satisfy the Triangle Inequality Theorem.
6. 1: 4 + 6 = 10 < 1. This option does not satisfy the Triangle Inequality Theorem.
7. 11: 4 + 6 = 10 < 11. This option satisfies the Triangle Inequality Theorem.

Therefore, the options that could be the third side of a triangle with the sides measuring 4 and 6 are 9 and 11.

Answer 2

pick one

Answer 3

Based on the given options, the third side of a triangle that could work with sides measuring 4 and 6 is 9 units.