Question

Can a triangle be formed with side lengths 3, 9, 17? Explain.

No, because 3 + 9 < 17
Yes, because 3 + 9 > 17
No, because 17 − 3 < 9
Yes, because 17 − 9 < 3

Answer 1

To determine if a triangle can be formed with side lengths 3, 9, and 17, we can use the triangle inequality theorem. This theorem 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 check the conditions for the side lengths 3, 9, and 17:

1. **3 + 9 > 17**:
- 12 > 17 (This is false)

2. **3 + 17 > 9**:
- 20 > 9 (This is true)

3. **9 + 17 > 3**:
- 26 > 3 (This is true)

Since the first condition (3 + 9 > 17) is false, the triangle inequality is not satisfied. Therefore, we cannot form a triangle with side lengths 3, 9, and 17.

Thus, the correct answer is: **No, because 3 + 9 < 17**.