Final answer:
To determine whether a set of numbers could represent the sides of a triangle, we need to check if they satisfy the triangle inequality theorem.
Step-by-step explanation:
A triangle is a polygon with three sides. To determine if a set of numbers could represent the sides of a triangle, we need to check if they satisfy the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
To apply this theorem to each set of numbers, we can take the three sides and check if the sum of the two smaller sides is greater than the largest side. By doing this for each set, we find that:
- a) 3, 4, 5: 3 + 4 = 7 > 5, 4 + 5 = 9 > 3, and 3 + 5 = 8 > 4. Therefore, this set can represent the sides of a triangle.
- b) 5, 12, 14: 5 + 12 = 17 > 14, 12 + 14 = 26 > 5, but 5 + 14 = 19 < 12. Therefore, this set cannot represent the sides of a triangle.
- c) 7, 24, 25: 7 + 24 = 31 > 25, 24 + 25 = 49 > 7, and 7 + 25 = 32 > 24. Therefore, this set can represent the sides of a triangle.
- d) 10, 15, 20: 10 + 15 = 25 > 20, 15 + 20 = 35 > 10, but 10 + 20 = 30 < 15. Therefore, this set cannot represent the sides of a triangle.
In conclusion, options a) and c) could represent the sides of a triangle.