Question

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

A {12, 19, 29}
B {12, 17, 31}
C {6, 10, 15}
D {9, 24, 30}

Answer 1

Set B {12, 17, 31} could not represent the sides of a triangle, as the sum of the two smaller sides is not greater than the third side, violating the triangle inequality theorem.

Step-by-step explanation:

To determine which sets of numbers could not represent the sides of a triangle, we must apply the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's apply this to the given sets:

• A {12, 19, 29} : 12 + 19 > 29 (31 > 29) – satisfies the triangle inequality theorem.
• B {12, 17, 31} : 12 + 17 > 31 (29 > 31) – does not satisfy the triangle inequality theorem.
• C {6, 10, 15} : 6 + 10 > 15 (16 > 15) – satisfies the triangle inequality theorem.
• D {9, 24, 30} : 9 + 24 > 30 (33 > 30) – satisfies the triangle inequality theorem.

Therefore, set B {12, 17, 31} could not represent the sides of a triangle, as it fails the triangle inequality test.