Which of the following sets of numbers could not represent the three sides of a triangle?

Question

Answer
Multiple Choice Answers
left curly bracket, 4, comma, 17, comma, 21, right curly bracket{4,17,21}
left curly bracket, 4, comma, 6, comma, 7, right curly bracket{4,6,7}
left curly bracket, 12, comma, 19, comma, 29, right curly bracket{12,19,29}
left curly bracket, 7, comma, 15, comma, 20, right curly bracket{7,15,20}

Answer 1

To determine which set of numbers cannot represent the sides of a triangle, we can use the triangle inequality theorem. This theorem states that for any triangle with sides $a$, $b$, and $c$:

1. $a+b>c$
2. $a+c>b$
3. $b+c>a$

We can check each set of numbers against these conditions:

1. Set {4, 17, 21}:

   • $4+17=21$ (not greater than)
   • This set does not satisfy the triangle inequality, so it cannot form a triangle.

2. Set {4, 6, 7}:

   • $4+6=10>7$
   • $4+7=11>6$
   • $6+7=13>4$
   • This set satisfies the triangle inequality.

3. Set {12, 19, 29}:

   • $12+19=31>29$
   • $12+29=41>19$
   • $19+29=48>12$
   • This set satisfies the triangle inequality.

4. Set {7, 15, 20}:

   • $7+15=22>20$
   • $7+20=27>15$
   • $15+20=35>7$
   • This set satisfies the triangle inequality.

The only set of numbers that could not represent the sides of a triangle is:

{4, 17, 21}.