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)
The options are:
9
1
2
11
Please answer it correctly.
AAAaannndd the bot gets it wrong yet again!
If the 3rd side is x, then you need
6-4 < x < 6+4
2 < x < 10
so 9 is the only choice
oops wrong question
To determine which option could be the third side of a triangle using the Triangle Inequality Theorem, we need to compare the sum of the lengths of the two given sides with the length of each of the options.
The Triangle Inequality Theorem states that 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 given lengths are 4 and 6.
Let's test the options by comparing their lengths with the sum of the given lengths:
1. 4 + 6 = 10, and 10 is greater than 1, so option 1 could be the third side of a triangle.
2. 4 + 6 = 10, and 10 is greater than 2, so option 2 could be the third side of a triangle.
3. 4 + 6 = 10, and 10 is not greater than 9, so option 9 cannot be the third side of a triangle.
4. 4 + 6 = 10, and 10 is less than 11, so option 11 cannot be the third side of a triangle.
Therefore, the options that could be the third side of a triangle are 1 and 2.