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