Question
Joanna has four straws with the following lengths in inches:Straw A: 7Straw B: 9Straw C: 3Straw D: 10Possible combinations of three strawsConsider all possible combinations of three straws out of the four: 1. Straws A, B, C (7, 9, 3)Is 7 + 9 > 3? Yes (16 > 3)Is 7 + 3 > 9? Yes (10 > 9)Is 9 + 3 > 7? Yes (12 > 7)This combination forms a triangle. 2. Straws A, B, D (7, 9, 10)Is 7 + 9 > 10? Yes (16 > 10)Is 7 + 10 > 9? Yes (17 > 9)Is 9 + 10 > 7? Yes (19 > 7)This combination forms a triangle. 3. Straws A, C, D (7, 3, 10)Is 7 + 3 > 10? No (10 is not greater than 10).This combination does not form a triangle. 4. Straws B, C, D (9, 3, 10)Is 9 + 3 > 10? Yes (12 > 10).Is 9 + 10 > 3? Yes (19 > 3)Is 3 + 10 > 9? Yes (13 > 9)This combination forms a triangle. ConclusionJoanna can make 3 different triangles. The combinations of straws she can use are:A, B, C (7, 9, 3)A, B, D (7, 9, 10)B, C, D (9, 3, 10)
Take all of that and make it more simple to understand
Take all of that and make it more simple to understand
Answers
GPT-4o mini
Sure! Here's a simpler breakdown of Joanna's straws and the triangles she can form:
**Straw lengths:**
- Straw A: 7 inches
- Straw B: 9 inches
- Straw C: 3 inches
- Straw D: 10 inches
**To see if three straws can form a triangle, we check:**
1. The sum of the lengths of any two straws must be greater than the length of the third straw.
**Possible combinations of three straws:**
1. **Straws A, B, C (7, 9, 3)**:
- 7 + 9 > 3? Yes (16 > 3)
- 7 + 3 > 9? Yes (10 > 9)
- 9 + 3 > 7? Yes (12 > 7)
- **This combination can form a triangle.**
2. **Straws A, B, D (7, 9, 10)**:
- 7 + 9 > 10? Yes (16 > 10)
- 7 + 10 > 9? Yes (17 > 9)
- 9 + 10 > 7? Yes (19 > 7)
- **This combination can form a triangle.**
3. **Straws A, C, D (7, 3, 10)**:
- 7 + 3 > 10? No (10 is not greater than 10)
- **This combination cannot form a triangle.**
4. **Straws B, C, D (9, 3, 10)**:
- 9 + 3 > 10? Yes (12 > 10)
- 9 + 10 > 3? Yes (19 > 3)
- 3 + 10 > 9? Yes (13 > 9)
- **This combination can form a triangle.**
**Conclusion:**
Joanna can make 3 different triangles with the following combinations of straws:
1. Straws A, B, C (7, 9, 3)
2. Straws A, B, D (7, 9, 10)
3. Straws B, C, D (9, 3, 10)
So, she can create a total of **3 triangles**.
**Straw lengths:**
- Straw A: 7 inches
- Straw B: 9 inches
- Straw C: 3 inches
- Straw D: 10 inches
**To see if three straws can form a triangle, we check:**
1. The sum of the lengths of any two straws must be greater than the length of the third straw.
**Possible combinations of three straws:**
1. **Straws A, B, C (7, 9, 3)**:
- 7 + 9 > 3? Yes (16 > 3)
- 7 + 3 > 9? Yes (10 > 9)
- 9 + 3 > 7? Yes (12 > 7)
- **This combination can form a triangle.**
2. **Straws A, B, D (7, 9, 10)**:
- 7 + 9 > 10? Yes (16 > 10)
- 7 + 10 > 9? Yes (17 > 9)
- 9 + 10 > 7? Yes (19 > 7)
- **This combination can form a triangle.**
3. **Straws A, C, D (7, 3, 10)**:
- 7 + 3 > 10? No (10 is not greater than 10)
- **This combination cannot form a triangle.**
4. **Straws B, C, D (9, 3, 10)**:
- 9 + 3 > 10? Yes (12 > 10)
- 9 + 10 > 3? Yes (19 > 3)
- 3 + 10 > 9? Yes (13 > 9)
- **This combination can form a triangle.**
**Conclusion:**
Joanna can make 3 different triangles with the following combinations of straws:
1. Straws A, B, C (7, 9, 3)
2. Straws A, B, D (7, 9, 10)
3. Straws B, C, D (9, 3, 10)
So, she can create a total of **3 triangles**.