Question

which set of numbers can not represent the lengths of the sides of a triangle?
a 6,8,11
b 7,5,6
c 7,18,11
d 9,12,19

Explanation:

Step1: Recall triangle inequality rule

For sides $a,b,c$, sum of any two sides > third side.

Step2: Test Option A

$6+8>11$ ($14>11$), $6+11>8$ ($17>8$), $8+11>6$ ($19>6$). All true.

Step3: Test Option B

$7+5>6$ ($12>6$), $7+6>5$ ($13>5$), $5+6>7$ ($11>7$). All true.

Step4: Test Option C

$7+11=18$, which is not > 18. Fails rule.

Step5: Verify Option D

$9+12>19$ ($21>19$), $9+19>12$ ($28>12$), $12+19>9$ ($31>9$). All true.

Answer:

C. 7,18,11