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


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Answer 1

To determine whether the given sets of sides can form a triangle, we apply the Triangle Inequality Theorem, which states that for any triangle with sides a, b, and c:

1. a + b > c
2. a + c > b
3. b + c > a

We will evaluate each set of values accordingly.

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
- **Answer: Yes**

2. **(a = 7, b = 10, c = 18)**
- 7 + 10 > 18 (17 > 18) → False
- Since one condition is false, the triangle cannot be formed.
- **Answer: No**

3. **(a = 2, b = 4, c = 7)**
- 2 + 4 > 7 (6 > 7) → False
- Since one condition is false, the triangle cannot be formed.
- **Answer: No**

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
- **Answer: Yes**

Final answers:
- a = 3, b = 2, c = 4: **Yes**
- a = 7, b = 10, c = 18: **No**
- a = 2, b = 4, c = 7: **No**
- a = 5, b = 4, c = 7: **Yes**