Given the numbers are measurments of the sides of a triagnle, for which of the following can a triangle exist?
1. 8,10,20
2.16,18,25
3.7,7,7
I say 2 & 3. Am I right?
<<Am I right? >> yes
To determine if a triangle can exist with the given side lengths, you can use 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.
Let's apply this theorem to each set of side lengths:
1. For the side lengths 8, 10, and 20:
- 8 + 10 = 18, which is less than 20.
- So, a triangle cannot be formed with these lengths.
2. For the side lengths 16, 18, and 25:
- 16 + 18 = 34, which is greater than 25.
- 16 + 25 = 41, which is also greater than 18.
- 18 + 25 = 43, which is greater than 16.
- So, a triangle can be formed with these lengths.
3. For the side lengths 7, 7, and 7:
- 7 + 7 = 14, which is greater than 7.
- 7 + 7 = 14, which is greater than 7.
- 7 + 7 = 14, which is greater than 7.
- So, a triangle can also be formed with these lengths.
Based on the analysis, your statement that a triangle can be formed with side lengths 16, 18, and 25 (option 2) as well as side lengths 7, 7, and 7 (option 3) is correct.