Which set of numbers could be the lengths of the sides of a triangle?

Question

A. { 6,7,13}

B. {5,5,11}

C. {12,13,20}

D. {3,6,9}

Answer 1

 

This requires use of the triangle inequality theorem.  It states that the sum of any 2 sides of a triangle must be larger than the third side.  This should hold true for all possibilities.  We will check the sides for all triangles given:

 

A:  6, 7, 13

 

     6 + 7 > 13

     13 > 13  ... FALSE ... so a triangle cannot have these measures

 

B:  5, 5, 11

 

     5 + 5 > 11

     10 > 11 ... FALSE ... so a triangle cannot have these measures

 

C:  12, 13, 20

 

     12 + 13 > 20

     25 > 20 ...TRUE

 

    12 + 20 > 13

    32 > 13 ... TRUE

 

    13 + 20 > 12

    23 > 12 ... TRUE

 

    Since all 3 cases for C are true, these are valid side measures for a triangle

 

D:  3, 6, 9

 

      3 + 6 > 9

      9 > 9 ... FALSE ... so a triangle cannot have these measures

 

THE ANSWER IS C 

Answer 2

Taking each set to be {A,B,C}, you need the set where A+B > C.  If A+B = C, they would make a line, and if A+B < C, no triangle is possible to draw with those numbers.