Question

construct a triangle or not.5, 10, 2

Answers

GPT-4o mini
To determine if a triangle can be constructed with the given side lengths of 5, 10, and 2, we can use the triangle inequality theorem. The triangle inequality states that for any triangle with sides \(a\), \(b\), and \(c\):

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Let's label the sides as follows:
- \(a = 5\)
- \(b = 10\)
- \(c = 2\)

Now we check each of the three inequalities:

1. \(5 + 10 > 2\)
- \(15 > 2\) (True)

2. \(5 + 2 > 10\)
- \(7 > 10\) (False)

3. \(10 + 2 > 5\)
- \(12 > 5\) (True)

Since the second inequality \(5 + 2 > 10\) is false, the given lengths (5, 10, and 2) cannot form a triangle.

### Conclusion:
A triangle cannot be constructed with the side lengths of 5, 10, and 2.