Question

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Question


Use the Triangle Inequality Theorem (see picture above) to solve this problem.

Two sides of a triangle measure 11 and 3. Identify the side measure that would NOT create a triangle.

(1 point)
Responses

7
7

9
9

12
12

13

Answer 1

To determine which side length would not create a triangle with the other two sides measuring 11 and 3, we can apply the Triangle Inequality Theorem. The theorem states that for any triangle with sides \(a\), \(b\), and \(c\), the following inequalities must hold:

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

Let’s denote the unknown side length as \(x\). We need to analyze each of the given options one by one and check whether they satisfy the Triangle Inequality Theorem.

### 1. Checking \(x = 7\):
- \(11 + 3 > 7\) → \(14 > 7\) (True)
- \(11 + 7 > 3\) → \(18 > 3\) (True)
- \(3 + 7 > 11\) → \(10 > 11\) (False)

This does not create a triangle.

### 2. Checking \(x = 9\):
- \(11 + 3 > 9\) → \(14 > 9\) (True)
- \(11 + 9 > 3\) → \(20 > 3\) (True)
- \(3 + 9 > 11\) → \(12 > 11\) (True)

This creates a triangle.

### 3. Checking \(x = 12\):
- \(11 + 3 > 12\) → \(14 > 12\) (True)
- \(11 + 12 > 3\) → \(23 > 3\) (True)
- \(3 + 12 > 11\) → \(15 > 11\) (True)

This creates a triangle.

### 4. Checking \(x = 13\):
- \(11 + 3 > 13\) → \(14 > 13\) (True)
- \(11 + 13 > 3\) → \(24 > 3\) (True)
- \(3 + 13 > 11\) → \(16 > 11\) (True)

This creates a triangle.

### Conclusion:
The side length that would NOT create a triangle is **7**.