Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle. 2, 3, 6 7, 5, 13 7, 8, 9 4, 8, 12
According to the Triangle Inequality Theorem, for a triangle to be formed, the sum of any two side lengths must be greater than the third side length.
Applying the theorem to the given side lengths:
For the first set of side lengths (2, 3, 6):
2 + 3 = 5 (not greater than 6)
3 + 6 = 9 (greater than 2)
2 + 6 = 8 (greater than 3)
Therefore, the side lengths 3, 6, and 2 cannot form a triangle.
For the second set of side lengths (7, 5, 13):
7 + 5 = 12 (greater than 13)
5 + 13 = 18 (not greater than 7)
7 + 13 = 20 (greater than 5)
Therefore, the side lengths 7, 5, and 13 cannot form a triangle.
For the third set of side lengths (7, 8, 9):
7 + 8 = 15 (greater than 9)
8 + 9 = 17 (greater than 7)
7 + 9 = 16 (greater than 8)
Therefore, the side lengths 7, 8, and 9 can form a triangle.
For the fourth set of side lengths (4, 8, 12):
4 + 8 = 12 (not greater than 12)
8 + 12 = 20 (greater than 4)
4 + 12 = 16 (greater than 8)
Therefore, the side lengths 4, 8, and 12 cannot form a triangle.
In summary, the set of side lengths that form a triangle is 7, 8, and 9.