Can a triangle have side lengths 2, 3, and 5?
To determine if a triangle can have side lengths 2, 3, and 5, 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.
So, in this case, we need to check if the sum of any two sides is greater than the third side:
1. Sum of the first two sides: 2 + 3 = 5
- Since 5 is not greater than 5, this condition is not met.
2. Sum of the first and third sides: 2 + 5 = 7
- Since 7 is greater than 3, this condition is met.
3. Sum of the second and third sides: 3 + 5 = 8
- Since 8 is greater than 2, this condition is met.
Based on the triangle inequality theorem, for a triangle to exist, each of the three conditions must be met. However, in this case, the first condition is not met, which means a triangle cannot have side lengths of 2, 3, and 5.