Apply the triangle inequality theorem and determine which group of sides measures will form a triangle
12, 10, 22
2, 7, 6
8, 1, 7
9, 4, 3
To determine if a group of sides can form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
1. For sides 12, 10, 22:
12 + 10 > 22 (True)
10 + 22 > 12 (True)
12 + 22 > 10 (True)
This group of sides can form a triangle.
2. For sides 2, 7, 6:
2 + 7 > 6 (True)
7 + 6 > 2 (True)
2 + 6 < 7 (False)
This group of sides cannot form a triangle.
3. For sides 8, 1, 7:
8 + 1 > 7 (True)
1 + 7 < 8 (False)
8 + 7 > 1 (True)
This group of sides cannot form a triangle.
4. For sides 9, 4, 3:
9 + 4 > 3 (True)
4 + 3 > 9 (False)
9 + 3 > 4 (True)
This group of sides cannot form a triangle.
Therefore, only sides 12, 10, 22 can form a triangle.