Question
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:
The sum of the lengths of any two straws must be greater than the length of the third straw.
Possible combinations of three straws:
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.
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.
Straws A, C, D (7, 3, 10):
7 + 3 > 10? No (10 is not greater than 10)
This combination cannot form a triangle.
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:
Straws A, B, C (7, 9, 3)
Straws A, B, D (7, 9, 10)
Straws B, C, D (9, 3, 10)
So, she can create a total of 3 triangles.
Take this and make it an explanation thats a little bit more like in a paragraph
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:
The sum of the lengths of any two straws must be greater than the length of the third straw.
Possible combinations of three straws:
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.
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.
Straws A, C, D (7, 3, 10):
7 + 3 > 10? No (10 is not greater than 10)
This combination cannot form a triangle.
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:
Straws A, B, C (7, 9, 3)
Straws A, B, D (7, 9, 10)
Straws B, C, D (9, 3, 10)
So, she can create a total of 3 triangles.
Take this and make it an explanation thats a little bit more like in a paragraph
Answers
GPT-4o mini
To determine which combinations of straws can form a triangle, we apply the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. Given the lengths of four straws—A (7 inches), B (9 inches), C (3 inches), and D (10 inches)—we can examine all possible sets of three straws.
The first combination, straws A, B, and C (7, 9, and 3 inches), satisfies the triangle inequality as all three conditions hold true: 7 + 9 > 3, 7 + 3 > 9, and 9 + 3 > 7. Thus, these straws can form a triangle. The second combination, straws A, B, and D (7, 9, and 10 inches), also meets the criteria, as 7 + 9 > 10, 7 + 10 > 9, and 9 + 10 > 7 are all valid. However, the combination of straws A, C, and D (7, 3, and 10 inches) fails because 7 + 3 is not greater than 10, disqualifying it from forming a triangle. In the last combination, straws B, C, and D (9, 3, and 10 inches) meet the conditions of the triangle inequality, allowing them to create a triangle as well.
In conclusion, Joanna can successfully form three distinct triangles using the following combinations of straws: A, B, and C; A, B, and D; and B, C, and D. Therefore, she has a total of three ways to create triangles with her straws.
The first combination, straws A, B, and C (7, 9, and 3 inches), satisfies the triangle inequality as all three conditions hold true: 7 + 9 > 3, 7 + 3 > 9, and 9 + 3 > 7. Thus, these straws can form a triangle. The second combination, straws A, B, and D (7, 9, and 10 inches), also meets the criteria, as 7 + 9 > 10, 7 + 10 > 9, and 9 + 10 > 7 are all valid. However, the combination of straws A, C, and D (7, 3, and 10 inches) fails because 7 + 3 is not greater than 10, disqualifying it from forming a triangle. In the last combination, straws B, C, and D (9, 3, and 10 inches) meet the conditions of the triangle inequality, allowing them to create a triangle as well.
In conclusion, Joanna can successfully form three distinct triangles using the following combinations of straws: A, B, and C; A, B, and D; and B, C, and D. Therefore, she has a total of three ways to create triangles with her straws.