Which of the following set of numbers could not represent the three sides of a triangle
4,16,17
8,20,25
13,16,30
The set of numbers that could not represent the three sides of a triangle is 13, 16, 30.
For a set of numbers to represent the sides of a triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the remaining side.
Let's check this for each set of numbers:
1. For 4, 16, and 17
- 4 + 16 > 17 (True)
- 4 + 17 > 16 (True)
- 16 + 17 > 4 (True)
All the conditions are met, so this set of numbers can represent the sides of a triangle.
2. For 8, 20, and 25
- 8 + 20 > 25 (True)
- 8 + 25 > 20 (True)
- 20 + 25 > 8 (True)
All the conditions are met, so this set of numbers can represent the sides of a triangle.
3. For 13, 16, and 30
- 13 + 16 > 30 (False)
The sum of the lengths of the two smaller sides (13 and 16) is not greater than the length of the largest side (30), so this set of numbers cannot represent the sides of a triangle.
Therefore, the set of numbers that could not represent the three sides of a triangle is 13, 16, 30.