Question

Which set of numbers may represent the lengths of the sides of a triangle?

A)5,8,13
B)6,17,22
C)16,24,7
D)26,8,15

Answer 1

The only set that may represent the lengths of the sides of a triangle is A) 5, 8, 13.

Step-by-step explanation:

The set of numbers that may represent the lengths of the sides of a triangle must satisfy the triangle inequality theorem. According to this theorem, 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 theorem to the given sets of numbers:

• A) 5, 8, 13: 5 + 8 = 13, which satisfies the triangle inequality theorem.
• B) 6, 17, 22: 6 + 17 = 23, which does not satisfy the triangle inequality theorem.
• C) 16, 24, 7: 7 + 16 = 23, which does not satisfy the triangle inequality theorem.
• D) 26, 8, 15: 8 + 15 = 23, which does not satisfy the triangle inequality theorem.

Therefore, only set A) 5, 8, 13 may represent the lengths of the sides of a triangle.