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

Let's evaluate each set of sides using the Triangle Inequality Theorem (a + b > c, a + c > b, and b + c > a) to determine if they can form a triangle.

1. **a = 3, b = 2, c = 4**
- Check:
- 3 + 2 > 4 → 5 > 4 (True)
- 3 + 4 > 2 → 7 > 2 (True)
- 2 + 4 > 3 → 6 > 3 (True)
- Result: Yes

2. **a = 7, b = 10, c = 18**
- Check:
- 7 + 10 > 18 → 17 > 18 (False)
- Result: No

3. **a = 2, b = 4, c = 7**
- Check:
- 2 + 4 > 7 → 6 > 7 (False)
- Result: No

4. **a = 5, b = 4, c = 7**
- Check:
- 5 + 4 > 7 → 9 > 7 (True)
- 5 + 7 > 4 → 12 > 4 (True)
- 4 + 7 > 5 → 11 > 5 (True)
- Result: Yes

Here are the answers summarized:

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**