The Triangle Inequality Theorem states that for any three sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's denote the side lengths as \(a = 3\) feet, \(b = 4\) feet, and \(c = 5\) feet. We need to check the following inequalities:
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)
Now, let's calculate each inequality:
- \(a + b = 3 + 4 = 7 > 5\) (True)
- \(a + c = 3 + 5 = 8 > 4\) (True)
- \(b + c = 4 + 5 = 9 > 3\) (True)
Since all three conditions are satisfied, the sides with lengths of 3 feet, 4 feet, and 5 feet do indeed form a triangle.