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)
1
11
2
9
AAAaannndd the bot gets it wrong yet again!
9
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.
In this case, we have two sides of lengths 4 and 6. Let's check the possible options:
1. If we consider the third side as 1, the sum of the first two sides is 4 + 6 = 10, which is greater than 1. So, yes, 1 could be the third side of a triangle.
2. If we consider the third side as 11, the sum of the first two sides is 4 + 6 = 10, which is not greater than 11. So, no, 11 could not be the third side of a triangle.
3. If we consider the third side as 2, the sum of the first two sides is 4 + 6 = 10, which is greater than 2. So, yes, 2 could be the third side of a triangle.
4. If we consider the third side as 9, the sum of the first two sides is 4 + 6 = 10, which is not greater than 9. So, no, 9 could not be the third side of a triangle.
Therefore, the options that could be the third side of a triangle are 1 and 2.