Question

select all of the sets of side lengths that will form a triangle.*
7, 6, 11
9, 5, 13
8, 3, 11
5, 5, 9
7, 7, 14

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 7, 6, 11

$7 + 6=13>11$, $7 + 11 = 18>6$, $6+11 = 17>7$. So, 7, 6, 11 can form a triangle.

Step3: Check 9, 5, 13

$9 + 5=14>13$, $9 + 13 = 22>5$, $5+13 = 18>9$. So, 9, 5, 13 can form a triangle.

Step4: Check 8, 3, 11

$8 + 3=11$, which is not greater than 11. So, 8, 3, 11 cannot form a triangle.

Step5: Check 5, 5, 9

$5 + 5=10>9$, $5 + 9 = 14>5$, $5+9 = 14>5$. So, 5, 5, 9 can form a triangle.

Step6: Check 7, 7, 14

$7 + 7=14$, which is not greater than 14. So, 7, 7, 14 cannot form a triangle.

Answer:

7, 6, 11; 9, 5, 13; 5, 5, 9