Question

2 of 142 of 14 Items 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. No, because 4+8 > 10, 8+10 > 4, and 10+4 > 8. Skip to navigation

Answer 1

To determine if Leo can make a triangle with the three straws measuring 4 inches, 8 inches, and 10 inches, 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.

Let's test the three conditions:

1. \( 4 + 8 > 10 \)
- \( 12 > 10 \) (True)

2. \( 8 + 10 > 4 \)
- \( 18 > 4 \) (True)

3. \( 10 + 4 > 8 \)
- \( 14 > 8 \) (True)

Since all three conditions are satisfied, the correct response is:

**Yes, because \( 4 + 8 > 10 \), \( 8 + 10 > 4 \), and \( 10 + 4 > 8 \).**