Question

Joanna has four straws of different lengths. The table shows the lengths of the straws. Straw A B C D Length in inches 7 9 3 10 Joanna makes as many triangles as she can using combinations of these straws. Which combination of straws can she use to make triangles? (Multiple answers can be selected.) (1 point)

Answer 1

To determine which combinations of straws can form triangles, we can use the triangle inequality theorem, which states that for any three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

The lengths of the straws are as follows:
- Straw A: 7 inches
- Straw B: 9 inches
- Straw C: 3 inches
- Straw D: 10 inches

Let's check all the combinations of three straws:

1. A, B, C (7, 9, 3):
- 7 + 9 > 3 (True)
- 7 + 3 > 9 (False)
- 9 + 3 > 7 (True)
- This combination cannot form a triangle.

2. A, B, D (7, 9, 10):
- 7 + 9 > 10 (False)
- 7 + 10 > 9 (True)
- 9 + 10 > 7 (True)
- This combination cannot form a triangle.

3. A, C, D (7, 3, 10):
- 7 + 3 > 10 (False)
- 7 + 10 > 3 (True)
- 3 + 10 > 7 (True)
- This combination cannot form a triangle.

4. B, C, D (9, 3, 10):
- 9 + 3 > 10 (False)
- 9 + 10 > 3 (True)
- 3 + 10 > 9 (True)
- This combination cannot form a triangle.

From the combinations checked above, none of the straws form a valid triangle based on the triangle inequality theorem. Therefore, Joanna cannot make any triangles with the given straws.