Question

Two sides of a triangle measure 11 and 3. Identify the side measure that would not create a triangle.(1 point)
Responses

9
9

12
12

7
7

13

Answer 1

To determine which side length would not create a triangle with the other two sides measuring 11 and 3, we can use the triangle inequality theorem. The theorem states that for any triangle with sides \( a \), \( b \), and \( c \):

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

Let's denote the third side as \( x \). The two sides we have are 11 and 3.

We will apply the triangle inequality:

1. \( 11 + 3 > x \) implies \( x < 14 \)
2. \( 11 + x > 3 \) simplifies to \( x > -8 \) (which is always true for positive sides)
3. \( 3 + x > 11 \) simplifies to \( x > 8 \)

From these inequalities, we have:
- \( x < 14 \)
- \( x > 8 \)

Now let's test the given options to see which value does not satisfy these conditions:

- **For 9**: \( 9 > 8 \) and \( 9 < 14 \) — valid side.
- **For 12**: \( 12 > 8 \) and \( 12 < 14 \) — valid side.
- **For 7**: \( 7 > 8 \) — invalid side (cannot form a triangle).
- **For 13**: \( 13 > 8 \) and \( 13 < 14 \) — valid side.

Thus, the side measure that would not create a triangle is **7**.