Question
Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Based on this theorem, answer the following question.
Leo has three straws. They are 4 inches, 8 inches, and 10 inches long. Can he make a triangle using these three straws?
(1 point)
Responses
We need more information to determine.
We need more information to determine.
Yes, because 4+8 > 10, 8+10 > 4, and 10+4 > 8.
Yes, because 4+8 > 10, 8+10 > 4, and 10+4 > 8.
No, because 4+8 > 10, 8+10 > 4, and 10+4 > 8.
Leo has three straws. They are 4 inches, 8 inches, and 10 inches long. Can he make a triangle using these three straws?
(1 point)
Responses
We need more information to determine.
We need more information to determine.
Yes, because 4+8 > 10, 8+10 > 4, and 10+4 > 8.
Yes, because 4+8 > 10, 8+10 > 4, and 10+4 > 8.
No, because 4+8 > 10, 8+10 > 4, and 10+4 > 8.
Answers
GPT-4o mini
To determine if Leo can make a triangle using the three straws with lengths 4 inches, 8 inches, and 10 inches, we can apply the Triangle Inequality Theorem.
We check the following conditions:
1. 4 + 8 > 10
2. 8 + 10 > 4
3. 10 + 4 > 8
Now let's evaluate these inequalities:
1. **4 + 8 = 12, and 12 > 10** (satisfied)
2. **8 + 10 = 18, and 18 > 4** (satisfied)
3. **10 + 4 = 14, and 14 > 8** (satisfied)
All three conditions are satisfied. Therefore, the correct response is:
**Yes, because 4 + 8 > 10, 8 + 10 > 4, and 10 + 4 > 8.**
We check the following conditions:
1. 4 + 8 > 10
2. 8 + 10 > 4
3. 10 + 4 > 8
Now let's evaluate these inequalities:
1. **4 + 8 = 12, and 12 > 10** (satisfied)
2. **8 + 10 = 18, and 18 > 4** (satisfied)
3. **10 + 4 = 14, and 14 > 8** (satisfied)
All three conditions are satisfied. Therefore, the correct response is:
**Yes, because 4 + 8 > 10, 8 + 10 > 4, and 10 + 4 > 8.**