To determine which group of numbers cannot form a triangle, we need to apply the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's analyze each group of numbers:
A. 4, 8, 5:
4 + 8 = 12 (which is greater than 5)
4 + 5 = 9 (which is greater than 8)
5 + 8 = 13 (which is greater than 4)
Since in this case, the sum of the two smaller sides is always greater than the third side, this group can form a triangle.
B. 3, 4, 5:
3 + 4 = 7 (which is greater than 5)
3 + 5 = 8 (which is greater than 4)
4 + 5 = 9 (which is greater than 3)
This group also satisfies the Triangle Inequality Theorem and can form a triangle.
C. 6, 6, 12:
6 + 6 = 12 (which is equal to 12)
6 + 12 = 18 (which is greater than 6)
6 + 12 = 18 (which is greater than 6)
Since the sum of the two smaller sides is equal to the third side, this group can also form a triangle (specifically an equilateral triangle).
D. 3, 3, 5:
3 + 3 = 6 (which is not greater than 5)
3 + 5 = 8 (which is greater than 3)
3 + 5 = 8 (which is greater than 3)
In this case, the sum of the two smaller sides (both 3) is not greater than the length of the third side (5). Therefore, this group (3, 3, 5) cannot form a triangle.
So, the correct answer is:
D. 3, 3, 5 (This group cannot form a triangle)
Answer: Choice C
Reason: A triangle is only possible when adding any two sides leads to something larger than the third side. Unfortunately choice C has 6+6 = 12 is not larger than the third side of 12. In other words 6+6 > 12 is false. Therefore, choice C will not form a triangle. Grab pieces of string to try it out for yourself.
For more information, search out "triangle inequality theorem".
