Question

which of the following sets of numbers could be the lengths of the sides of a triangle? select three correct answers. 4,22,15 1,23,20 55,18,22 18,11,11 11,4,14 23,23,13

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 4, 22, 18

$4 + 18=22$, which does not satisfy the triangle - inequality theorem since $4 + 18$ is not greater than $22$.

Step3: Check set 1, 23, 20

$1+20 = 21<23$, does not satisfy the triangle - inequality theorem.

Step4: Check set 55, 16, 22

$16 + 22=38<55$, does not satisfy the triangle - inequality theorem.

Step5: Check set 18, 11, 11

$11+11 = 22>18$, $11 + 18>11$, $18+11>11$, satisfies the triangle - inequality theorem.

Step6: Check set 11, 4, 14

$4+11 = 15>14$, $4 + 14>11$, $11+14>4$, satisfies the triangle - inequality theorem.

Step7: Check set 23, 23, 13

$13+23>23$, $23 + 23>13$, $23+13>23$, satisfies the triangle - inequality theorem.

Answer:

18, 11, 11; 11, 4, 14; 23, 23, 13