To determine which of the given sets of numbers can form a triangle, we need to check if they satisfy the triangle inequality theorem.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's check each set of numbers:
A: 3, 3, 6
The sum of the two smaller sides is 3 + 3 = 6, which is equal to the longer side. According to the triangle inequality theorem, in order for a triangle to be formed, the sum of the two smaller sides must be greater than the length of the longer side. In this case, 6 > 6, which means this set of numbers cannot form a triangle.
B: 6, 8, 10
The sum of the two smaller sides is 6 + 8 = 14, which is greater than the longer side of 10. This set of numbers satisfies the triangle inequality theorem and can form a triangle.
C: 4, 6, 13
The sum of the two smaller sides is 4 + 6 = 10, which is less than the longer side of 13. According to the triangle inequality theorem, the sum of the two smaller sides must be greater than the length of the longer side for a triangle to be formed. In this case, 10 < 13, so this set of numbers cannot form a triangle.
Therefore, set B: 6, 8, 10 can form a triangle.