Question

Use the triangle inequity to see which set pf side lengths will form a triangle.
A: 4, 1, and 6.
B: 8, 6, and 2.
Or C: 5, 2, and 4.

Answer 1

The triangle inequality theorem states that for three lengths to form a triangle, the sum of any two lengths must be greater than the third length. We will analyze each set of side lengths according to this rule.

**A: 4, 1, and 6**
1. \(4 + 1 = 5 > 6\) (False)
2. \(4 + 6 = 10 > 1\) (True)
3. \(1 + 6 = 7 > 4\) (True)

Since 4 + 1 is not greater than 6, these lengths **cannot** form a triangle.

---

**B: 8, 6, and 2**
1. \(8 + 6 = 14 > 2\) (True)
2. \(8 + 2 = 10 > 6\) (True)
3. \(6 + 2 = 8 \not> 8\) (False)

Since 6 + 2 is not greater than 8, these lengths **cannot** form a triangle.

---

**C: 5, 2, and 4**
1. \(5 + 2 = 7 > 4\) (True)
2. \(5 + 4 = 9 > 2\) (True)
3. \(2 + 4 = 6 > 5\) (True)

All conditions are satisfied, so these lengths **can** form a triangle.

---

**Conclusion:**
- Set A (4, 1, 6) cannot form a triangle.
- Set B (8, 6, 2) cannot form a triangle.
- Set C (5, 2, 4) can form a triangle.