{ 13, 9, 6} represent the sides of a triangle
Solution:
Use the triangle inequality law
The sum of the lengths of any two sides of a triangle must be greater than the third side
Option A
{13, 9, 6}
[tex]13 + 9 > 6\\\\22 > 6[/tex]
Also,
[tex]9+6>13\\\\15>13[/tex]
Thus, sum of length of any two sides is greater than third side
Therefore, { 13, 9, 6} represent the sides of a triangle
Option B
{12, 7, 20}
[tex]12+7>20\\[/tex]
19 is not greater than 20
Therefore, {12, 7, 20} does not represent the sides of a triangle
Option C
{25, 50, 75}
[tex]25+50>75\\[/tex]
75 is equal to 75
Therefore, {25, 50, 75} does not represent the sides of a triangle
