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}.