1) Which of the following ingegers can not represent the lengths of the sides of a triangle?
(9,10,11) (4.7,9) (4,8,12) & (6,6,11)
Try drawing the 4,8,12 triangle. Have fun.
any two sides must be longer than the third.
Example with set 1.
9+10>11
10+11>9
11+9>10
To determine which of the given sets of integers can represent the lengths of the sides of a triangle, we can use 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 set of integers:
1) (9, 10, 11):
- 9 + 10 > 11: True
- 10 + 11 > 9: True
- 11 + 9 > 10: True
The set (9, 10, 11) can represent the lengths of the sides of a triangle.
2) (4.7, 9):
We need three sides for a triangle, so this set does not meet the requirements. It cannot represent the lengths of the sides of a triangle.
3) (4, 8, 12):
- 4 + 8 > 12: False
- 4 + 12 > 8: True
- 8 + 12 > 4: True
The set (4, 8, 12) cannot represent the lengths of the sides of a triangle.
4) (6, 6, 11):
- 6 + 6 > 11: False
- 6 + 11 > 6: True
- 6 + 11 > 6: True
The set (6, 6, 11) cannot represent the lengths of the sides of a triangle.
Therefore, the sets that can represent the lengths of the sides of a triangle are (9, 10, 11).