Which group of sides can make a triangle?
Responses
3, 12, and 8
3, 12, and 8 - incorrect
6, 4, and 10
6, 4, and 10 - no response given
5, 9, and 6
3 answers
5, 9, and 6 - correct
why is 5, 9, and 6 correct?
The lengths of the sides in a triangle must satisfy the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we can check if the lengths 5, 9, and 6 satisfy this theorem:
- 5 + 9 > 6 is true (5 + 9 = 14 > 6)
- 5 + 6 > 9 is true (5 + 6 = 11 > 9)
- 9 + 6 > 5 is true (9 + 6 = 15 > 5)
Since all three conditions hold true, 5, 9, and 6 can make a triangle.
In this case, we can check if the lengths 5, 9, and 6 satisfy this theorem:
- 5 + 9 > 6 is true (5 + 9 = 14 > 6)
- 5 + 6 > 9 is true (5 + 6 = 11 > 9)
- 9 + 6 > 5 is true (9 + 6 = 15 > 5)
Since all three conditions hold true, 5, 9, and 6 can make a triangle.