Question

Joanna has four straws of different lengths. The table shows the lengths of the straws.Length of StrawsStraw ABCDLength in inches 7 9 3 10Joanna makes as many triangles as she can using combinations of three of these straws. Determine how many different triangles she can make. What combinations of straws does she use? Show your work.(4 points) make this sound like a 6th grader and do NOT plagiarize

Answer 1

First I wrote the lengths with their straw names:
- A = 7 in, B = 9 in, C = 3 in, D = 10 in.

Rule I used: To make a triangle the sum of the two shorter sides must be greater than the longest side.

Check each group of three straws (there are 4 choose 3 = 4 groups):

1) A, B, C = 7, 9, 3 (sorted 3, 7, 9): 3 + 7 = 10, and 10 > 9 → Triangle works.
2) A, B, D = 7, 9, 10 (sorted 7, 9, 10): 7 + 9 = 16, and 16 > 10 → Triangle works.
3) A, C, D = 7, 3, 10 (sorted 3, 7, 10): 3 + 7 = 10, but 10 = 10 → NOT a triangle (just straight line).
4) B, C, D = 9, 3, 10 (sorted 3, 9, 10): 3 + 9 = 12, and 12 > 10 → Triangle works.

Answer: Joanna can make 3 different triangles. The successful combinations are A-B-C (7, 9, 3), A-B-D (7, 9, 10), and B-C-D (9, 3, 10).