Question

Which of the following sets of numbers can be used as the lengths of the sides of a triangle?

• A. [5, 7, 9]
• B. [2, 4, 10]
• C. [5, 7, 12]
• D. [7, 9, 17]

Answer 1

The Correct Option is A

To determine which set of numbers can be used as the lengths of the sides of a triangle, we need to 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. We will test each option to see if it satisfies this theorem. 

1. Option [5, 7, 9]:
   • Check if \(5 + 7 > 9\): \(12 > 9\), which is true.
   • Check if \(5 + 9 > 7\): \(14 > 7\), which is true.
   • Check if \(7 + 9 > 5\): \(16 > 5\), which is true.
2. Option [2, 4, 10]:
   • Check if \(2 + 4 > 10\): \(6 > 10\), which is false.
3. Option [5, 7, 12]:
   • Check if \(5 + 7 > 12\): \(12 = 12\), which does not satisfy the inequality.
4. Option [7, 9, 17]:
   • Check if \(7 + 9 > 17\): \(16 > 17\), which is false.

Therefore, the only set of numbers that can be the lengths of the sides of a triangle is [5, 7, 9].