In a triangle, the lengths of any two sides must sum to be greater than the length of the third side. To identify which side length would not create a triangle with the two given sides (11 and 3), we can use the Triangle Inequality Theorem.
Let's denote the unknown side as \( x \).
According to the Triangle Inequality Theorem, we must satisfy the following conditions:
- \( 11 + 3 > x \) → \( 14 > x \) → \( x < 14 \)
- \( 11 + x > 3 \) → \( x > -8 \) (This condition is always satisfied since \( x \) must be a positive length.)
- \( 3 + x > 11 \) → \( x > 8 \)
Combining the valid inequalities, we get:
- \( 8 < x < 14 \)
Now, let's evaluate the given options: 7, 9, 12, and 13.
- For \( x = 7 \): This does not satisfy \( 8 < x \), so it will not create a triangle.
- For \( x = 9 \): This satisfies \( 8 < 9 < 14 \), so it can form a triangle.
- For \( x = 12 \): This also satisfies \( 8 < 12 < 14 \), so it can form a triangle.
- For \( x = 13 \): This satisfies \( 8 < 13 < 14 \), so it can form a triangle.
Therefore, the side measure that would NOT create a triangle is 7.
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