Question

1. which of the following side lengths would not form a triangle? 8,5,9 12,10,22 9,10,11 6,10,3

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: Check option 1 (8, 5, 9)

$8 + 5=13>9$, $8 + 9 = 17>5$, $5+9 = 14>8$. So, it can form a triangle.

Step3: Check option 2 (12, 10, 22)

$12 + 10=22$, which is not greater than 22. So, it cannot form a triangle.

Step4: Check option 3 (9, 10, 11)

$9 + 10 = 19>11$, $9+11 = 20>10$, $10 + 11=21>9$. So, it can form a triangle.

Step5: Check option 4 (6, 10, 3)

$6+3 = 9<10$. So, it cannot form a triangle.

Answer:

12, 10, 22; 6, 10, 3