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.

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.

Answer 1

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.