Question

Determine whether each set of numbers can represent the sides of a triangle:

{13, 9, 6}
{12, 7, 20}
{25, 50, 75}

Answer 1

{ 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}

$13 + 9 > 6\\\\22 > 6$

Also,

$9+6>13\\\\15>13$

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}

$12+7>20$

19 is not greater than 20

Therefore, {12, 7, 20} does not represent the sides of a triangle

Option C

{25, 50, 75}

$25+50>75$

75 is equal to 75

Therefore, {25, 50, 75} does not represent the sides of a triangle