To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's try to make triangles using each straw as the longest side:
1) A as the longest side: B + C > A (9 + 3 > 7) - This is true, so A, B, and C can form a triangle.
2) A as the longest side: B + D > A (9 + 10 > 7) - This is true, so A, B, and D can form a triangle.
3) A as the longest side: C + D > A (3 + 10 > 7) - This is true, so A, C, and D can form a triangle.
Next, let's try B as the longest side:
4) B as the longest side: A + C > B (7 + 3 > 9) - This is true, so B, A, and C can form a triangle.
5) B as the longest side: A + D > B (7 + 10 > 9) - This is true, so B, A, and D can form a triangle.
Finally, let's try C as the longest side:
6) C as the longest side: A + B > C (7 + 9 > 3) - This is true, so C, A, and B can form a triangle.
Therefore, Joanna can form 6 different triangles using combinations of three straws:
1) (A, B, C)
2) (A, B, D)
3) (A, C, D)
4) (B, A, C)
5) (B, A, D)
6) (C, A, B)
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 three of these straws. Determine how many different triangles she can make. What combinations of straws does she use? Show your work.
1 answer