According to the triangle inequality theorem, which set of 3 lengths cannot be the sides of the triangle?
1. 10, 24, 26
2. 12,16,30
3. 20,15,35
4. 21, 26, 46
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the set of 3 lengths that cannot be the sides of a triangle would violate this rule.
2. 12, 16, 30: (12 + 16 = 28) (greater than 30) (12 + 30 = 42) (greater than 16) (16 + 30 = 46) (greater than 12)
This set violates the triangle inequality theorem.
Therefore, the set of 3 lengths that cannot be the sides of a triangle is the second set: 12, 16, 30.
