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 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. No, because the sum of any two sides is less than the third side. Yes, because the sum of any two sides is greater than the third side.

Answer 1

To determine if sides with lengths of 3 feet, 4 feet, and 5 feet can form a triangle, we can apply the Triangle Inequality Theorem. According to this theorem, for three lengths \(a\), \(b\), and \(c\) to form a triangle, the following conditions must all be satisfied:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Let's check these conditions with the given side lengths (3, 4, and 5):

1. \(3 + 4 > 5\) → \(7 > 5\) (true)
2. \(3 + 5 > 4\) → \(8 > 4\) (true)
3. \(4 + 5 > 3\) → \(9 > 3\) (true)

Since all three conditions are satisfied, we conclude that the side lengths 3 feet, 4 feet, and 5 feet do indeed form a triangle.

The correct response is: Yes, because the sum of any two sides is greater than the third side.