Question

15 multiple choice which of the following could represent the side lengths of a triangle? check all that apply 12, 22, 14 34, 9, 25 19,11, 17 23, 28, 52

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 12, 22, 14

$12 + 14=26>22$, $12 + 22 = 34>14$, $14+22 = 36>12$. So, 12, 22, 14 can be side - lengths of a triangle.

Step3: Check 34, 9, 25

$9 + 25=34$, which is not greater than 34. So, 34, 9, 25 cannot be side - lengths of a triangle.

Step4: Check 19, 11, 17

$11 + 17 = 28>19$, $11+19 = 30>17$, $17 + 19=36>11$. So, 19, 11, 17 can be side - lengths of a triangle.

Step5: Check 23, 28, 52

$23+28 = 51<52$. So, 23, 28, 52 cannot be side - lengths of a triangle.

Answer:

12, 22, 14; 19, 11, 17