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)
2
11
1
9
In order for a set of three side lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Using the Triangle Inequality Theorem, we can see if the third side options would work:
1) Third side = 2
4 + 2 > 6 (True)
6 + 2 > 4 (True)
Therefore, the third side of 2 could be the third side of a triangle with side lengths of 4 and 6.
2) Third side = 11
4 + 11 > 6 (True)
6 + 11 > 4 (True)
Therefore, the third side of 11 could be the third side of a triangle with side lengths of 4 and 6.
3) Third side = 1
4 + 1 > 6 (False)
6 + 1 > 4 (True)
Therefore, the third side of 1 could not be the third side of a triangle with side lengths of 4 and 6.
4) Third side = 9
4 + 9 > 6 (True)
6 + 9 > 4 (True)
Therefore, the third side of 9 could be the third side of a triangle with side lengths of 4 and 6.
Based on the Triangle Inequality Theorem, the options of 2, 11, and 9 could all be the third side of a triangle with side lengths of 4 and 6.