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

Question

Answer
Multiple Choice Answers
left curly bracket, 13, comma, 27, comma, 41, right curly bracket{13,27,41}
left curly bracket, 11, comma, 14, comma, 24, right curly bracket{11,14,24}
left curly bracket, 15, comma, 22, comma, 35, right curly bracket{15,22,35}
left curly bracket, 12, comma, 22, comma, 32, right curly bracket{12,22,32}

Answer 1

To determine if a set of numbers can 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 \( c \), the following inequalities must be satisfied:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

We can check each set of numbers to see if any of these inequalities are violated.

1. Set {13, 27, 41}:

   • \( 13 + 27 = 40 \) (not greater than 41)
   • This set cannot represent the sides of a triangle.

2. Set {11, 14, 24}:

   • \( 11 + 14 = 25 > 24 \)
   • \( 11 + 24 = 35 > 14 \)
   • \( 14 + 24 = 38 > 11 \)
   • This set can represent the sides of a triangle.

3. Set {15, 22, 35}:

   • \( 15 + 22 = 37 > 35 \)
   • \( 15 + 35 = 50 > 22 \)
   • \( 22 + 35 = 57 > 15 \)
   • This set can represent the sides of a triangle.

4. Set {12, 22, 32}:

   • \( 12 + 22 = 34 > 32 \)
   • \( 12 + 32 = 44 > 22 \)
   • \( 22 + 32 = 54 > 12 \)
   • This set can represent the sides of a triangle.

Thus, the set that could not represent the sides of a triangle is:

{13, 27, 41}.