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 select all of the sets of side lengths that will form a triangle. 30,40,50 11,22,33 40,41,80 33,44,88 100,199,298

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 the set 7, 6, 11

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

Step3: Check the set 9, 5, 13

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

Step4: Check the set 8, 3, 11

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

Step5: Check the set 5, 5, 9

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

Step6: Check the set 7, 7, 14

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

Step7: Check the set 30, 40, 50

$30 + 40=70>50$, $30 + 50 = 80>40$, $40+50 = 90>30$. So, it can form a triangle.

Step8: Check the set 11, 22, 33

$11 + 22=33$, which is not greater than 33. So, it cannot form a triangle.

Step9: Check the set 40, 41, 80

$40 + 41=81>80$, $40 + 80 = 120>41$, $41+80 = 121>40$. So, it can form a triangle.

Step10: Check the set 33, 44, 88

$33 + 44=77<88$. So, it cannot form a triangle.

Step11: Check the set 100, 199, 298

$100 + 199=299>298$, $100 + 298 = 398>199$, $199+298 = 497>100$. So, it can form a triangle.

Answer:

7, 6, 11; 9, 5, 13; 5, 5, 9; 30, 40, 50; 40, 41, 80; 100, 199, 298