Question

Apply the Triangle Inequality Theorem to determine if sides with lengths of 3 feet, 4 feet, and 5 feet form a triangle.(1 point) Responses Yes, because the sum of any two sides is greater than the third side. Yes, because the sum of any two sides is greater than the third side. Yes, because the sum of any two sides is less than the third side. Yes, because the sum of any two sides is less than the third side. No, because two out of three conditions are met. No, because two out of three conditions are met. No, because the sum of any two sides is less than the third side.

Answer 1

To determine if the lengths 3 feet, 4 feet, and 5 feet can form a triangle, we need to apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check the three conditions:

1. **3 feet + 4 feet > 5 feet**:
\(3 + 4 = 7\) which is greater than 5. ✔️

2. **3 feet + 5 feet > 4 feet**:
\(3 + 5 = 8\) which is greater than 4. ✔️

3. **4 feet + 5 feet > 3 feet**:
\(4 + 5 = 9\) which is greater than 3. ✔️

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

**Yes, because the sum of any two sides is greater than the third side.**