Question

which set of side lengths does not form a triangle? all lengths are given in inches. (1 point)
11, 19, 9
18, 11, 8
9, 17, 11
18, 10, 8

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 (11, 19, 9)

$11 + 9=20>19$, $11 + 19 = 30>9$, $9+19 = 28>11$. This set can form a triangle.

Step3: Check option 2 (18, 11, 8)

$11 + 8=19>18$, $11 + 18=29>8$, $8 + 18=26>11$. This set can form a triangle.

Step4: Check option 3 (9, 17, 11)

$9+11 = 20>17$, $9 + 17=26>11$, $11+17 = 28>9$. This set can form a triangle.

Step5: Check option 4 (18, 10, 8)

$10 + 8=18$, which is not greater than 18. According to the triangle - inequality theorem, this set does not form a triangle.

Answer:

18, 10, 8