Question

joanna has four straws of different lengths. the table shows the lengths of the straws. length of 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 all of your work for credit. (either type your work in the text box below or upload an image.) (4 points)

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: List all combinations

The combinations of choosing 3 straws out of 4 are: (A, B, C), (A, B, D), (A, C, D), (B, C, D).

Step3: Check each combination

• For (A = 7, B = 9, C = 3): $7+9>3$, $7 + 3>9$, $9+3>7$. This combination can form a triangle.
• For (A = 7, B = 9, D = 10): $7+9>10$, $7 + 10>9$, $9+10>7$. This combination can form a triangle.
• For (A = 7, C = 3, D = 10): $7+3 = 10$, which does not satisfy the triangle - inequality theorem. This combination cannot form a triangle.
• For (B = 9, C = 3, D = 10): $9+3>10$, $9 + 10>3$, $3+10>9$. This combination can form a triangle.

Answer:

She can make 3 different triangles. The combinations are (A, B, C), (A, B, D), (B, C, D).