Using the Triangle Inequality Theorem (see picture above), determine which three sides form a triangle.

Question

(1 point)
Responses

8, 8, 20
8, 8, 20

10, 20, 30
10, 20, 30

10, 15, 20
10, 15, 20

4, 8, 12

Answer 1

To determine which sets of sides can form a triangle, we can use the Triangle Inequality Theorem. This theorem states that, for any three sides of a triangle (a, b, c), the following conditions must be satisfied:

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

Let’s analyze each set of sides given in your response:

1. Sides: 8, 8, 20

   • \(8 + 8 = 16\) which is not greater than 20. (Fails)
   • This set does not satisfy the Triangle Inequality Theorem.

2. Sides: 10, 20, 30

   • \(10 + 20 = 30\) which is not greater than 30. (Fails)
   • This set does not satisfy the Triangle Inequality Theorem.

3. Sides: 10, 15, 20

   • \(10 + 15 = 25\) which is greater than 20
   • \(10 + 20 = 30\) which is greater than 15
   • \(15 + 20 = 35\) which is greater than 10
   • This set satisfies the Triangle Inequality Theorem.

4. Sides: 4, 8, 12

   • \(4 + 8 = 12\) which is not greater than 12. (Fails)
   • This set does not satisfy the Triangle Inequality Theorem.

The only set of sides that can form a triangle is 10, 15, 20.