Question

which sets of side lengths form a triangle? all lengths are given in inches. (choose 3 answers.) (1 point) 9, 17, 11 11, 19, 9 18, 10, 8 18, 11, 8

Explanation:

Step1: Recall triangle - inequality theorem

For three side - lengths \(a\), \(b\), and \(c\) of a triangle, the following three inequalities must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check the set \(9,17,11\)

\(9+17 = 26>11\), \(9 + 11=20>17\), \(17+11 = 28>9\). So, it forms a triangle.

Step3: Check the set \(11,19,9\)

\(11+19=30>9\), \(11 + 9=20>19\), \(19+9 = 28>11\). So, it forms a triangle.

Step4: Check the set \(18,10,8\)

\(10 + 8=18\), which does not satisfy the triangle - inequality theorem (\(a + b>c\)). So, it does not form a triangle.

Step5: Check the set \(18,11,8\)

\(11+8 = 19>18\), \(11+18=29>8\), \(18 + 8=26>11\). So, it forms a triangle.

Answer:

9, 17, 11; 11, 19, 9; 18, 11, 8