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 straws, determine how many different triangles she can make.
(1 point)
2 triangles
3 triangles
4 triangles

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 of three - straw lengths

The combinations of lengths from straws A = 7, B = 9, C = 3, D = 10 are: (7, 9, 3), (7, 9, 10), (7, 3, 10), (9, 3, 10).

Step3: Check each combination against the triangle - inequality theorem

• For (7, 9, 3): $7 + 9>3$, $7+3 > 9$, $9 + 3>7$, so it can form a triangle.
• For (7, 9, 10): $7 + 9>10$, $7+10 > 9$, $9 + 10>7$, so it can form a triangle.
• For (7, 3, 10): $7+3=10$, which does not satisfy the triangle - inequality theorem, so it cannot form a triangle.
• For (9, 3, 10): $9 + 3>10$, $9+10 > 3$, $3 + 10>9$, so it can form a triangle.

Answer:

3 triangles