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, 15

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 set 7, 6, 11

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

Step3: Check set 9, 5, 13

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

Step4: Check set 8, 3, 11

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

Step5: Check set 5, 5, 9

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

Step6: Check set 7, 7, 15

$7+7 = 14<15$. So, it cannot form a triangle.

Answer:

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