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.

answers:

2

9

11

1

Answer 1

pick one.

Answer 2

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 remaining side.

Let's check each option:

1) The sum of 4 and 6 is 10, which is greater than 1. This option could be the third side of a triangle.

2) The sum of 4 and 6 is 10, which is greater than 2. This option could be the third side of a triangle.

3) The sum of 4 and 6 is 10, which is NOT greater than 9. This option cannot be the third side of a triangle.

4) The sum of 4 and 6 is 10, which is greater than 11. This option could be the third side of a triangle.

Therefore, the options that could be the third side of a triangle are:

1) 2
2) 9
4) 11

Answer 3

Based on the triangle inequality theorem, the third side of a triangle with the first two sides measuring 4 and 6 could be either 2 or 11.