Question

Triangles unit test
Apply the triangle inequality theorem to determine if sides with lengths of 3 feet, 4 feet, and 5 feet form a triangle

Answer 1

The triangle inequality theorem states that for any three sides of a triangle with lengths \(a\), \(b\), and \(c\), the following conditions must be satisfied:

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

Given the sides with lengths 3 feet, 4 feet, and 5 feet, we can label them as follows:
- \(a = 3\)
- \(b = 4\)
- \(c = 5\)

Now, we will check each of the triangle inequalities:

1. **Check \(a + b > c\)**:
\[
3 + 4 = 7 > 5 \quad \text{(true)}
\]

2. **Check \(a + c > b\)**:
\[
3 + 5 = 8 > 4 \quad \text{(true)}
\]

3. **Check \(b + c > a\)**:
\[
4 + 5 = 9 > 3 \quad \text{(true)}
\]

Since all three conditions of the triangle inequality theorem are satisfied, the sides with lengths 3 feet, 4 feet, and 5 feet do indeed form a triangle.