Question

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

Explanation:

To determine if three side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side) form a triangle, the triangle inequality theorem must hold: \(a + b>c\). We check each option:

Step 1: Check \(18, 11, 8\)

Longest side \(c = 18\). Sum of other two sides: \(11 + 8=19\). Since \(19>18\), this forms a triangle.

Step 2: Check \(18, 10, 8\)

Longest side \(c = 18\). Sum of other two sides: \(10 + 8 = 18\). But \(18\) is not greater than \(18\) (it's equal), so this does not satisfy the triangle inequality theorem and does not form a triangle.

Step 3: Check \(9, 17, 11\)

Longest side \(c = 17\). Sum of other two sides: \(9+11 = 20\). Since \(20>17\), this forms a triangle.

Step 4: Check \(11, 19, 9\)

Longest side \(c = 19\). Sum of other two sides: \(11 + 9=20\). Since \(20>19\), this forms a triangle.

Answer:

\(\boldsymbol{18, 10, 8}\) (the option with side lengths 18, 10, 8 inches)