Question

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side. a + b > c Using this theorem, tell whether the examples below are possible triangles by selecting yes or no. (4 points) Yes No a = 3, b = 2, c = 4 a = 7, b = 10, c = 18 a = 2, b = 4, c = 7 a = 5, b = 4, c = 7

Answer 1

To determine whether the given sets of sides can form a triangle based on the Triangle Inequality Theorem (a + b > c, a + c > b, and b + c > a), we'll check each case one by one.

1. **a = 3, b = 2, c = 4**
- \(3 + 2 > 4\) → 5 > 4 (True)
- \(3 + 4 > 2\) → 7 > 2 (True)
- \(2 + 4 > 3\) → 6 > 3 (True)
- Since all conditions are satisfied, **Yes**, it is a possible triangle.

2. **a = 7, b = 10, c = 18**
- \(7 + 10 > 18\) → 17 > 18 (False)
- Since one condition is not satisfied, **No**, it is not a possible triangle.

3. **a = 2, b = 4, c = 7**
- \(2 + 4 > 7\) → 6 > 7 (False)
- Since one condition is not satisfied, **No**, it is not a possible triangle.

4. **a = 5, b = 4, c = 7**
- \(5 + 4 > 7\) → 9 > 7 (True)
- \(5 + 7 > 4\) → 12 > 4 (True)
- \(4 + 7 > 5\) → 11 > 5 (True)
- Since all conditions are satisfied, **Yes**, it is a possible triangle.

To summarize:

1. a = 3, b = 2, c = 4 - **Yes**
2. a = 7, b = 10, c = 18 - **No**
3. a = 2, b = 4, c = 7 - **No**
4. a = 5, b = 4, c = 7 - **Yes**