Question

Which of the following sets of numbers could represent the three sides of a triangle?
Answer
Multiple Choice Answers
left curly bracket, 6, comma, 14, comma, 21, right curly bracket{6,14,21}
left curly bracket, 14, comma, 27, comma, 42, right curly bracket{14,27,42}
left curly bracket, 6, comma, 19, comma, 25, right curly bracket{6,19,25}
left curly bracket, 8, comma, 18, comma, 23, right curly bracket{8,18,23}

Answer 1

Use the triangle inequality: the sum of any two sides must be greater than the third.

- {6, 14, 21}: 6 + 14 = 20 ≤ 21 → no
- {14, 27, 42}: 14 + 27 = 41 ≤ 42 → no
- {6, 19, 25}: 6 + 19 = 25 = 25 → degenerate (not a triangle)
- {8, 18, 23}: 8 + 18 = 26 > 23, and the other two sums are also greater → yes

So {8, 18, 23} is the only valid triangle.