Which of the following sets of numbers could represent the three sides of a triangle?

Question

Answer
Multiple Choice Answers
left curly bracket, 15, comma, 25, comma, 39, right curly bracket{15,25,39}
left curly bracket, 5, comma, 9, comma, 16, right curly bracket{5,9,16}
left curly bracket, 5, comma, 14, comma, 19, right curly bracket{5,14,19}
left curly bracket, 9, comma, 23, comma, 33, right curly bracket{9,23,33}

Answer 1

To determine whether a set of three numbers can represent the sides of a triangle, we can use the triangle inequality theorem. This theorem states that for any three sides $a$, $b$, and $c$ of a triangle, the following conditions must be met:

1. $a+b>c$
2. $a+c>b$
3. $b+c>a$

Let’s evaluate each set of numbers:

1. Set {15, 25, 39}

   • $15+25=40>39$ (True)
   • $15+39=54>25$ (True)
   • $25+39=64>15$ (True)
   • All conditions are satisfied, so this set can form a triangle.

2. Set {5, 9, 16}

   • $5+9=14<16$ (False)
   • Since the first condition fails, this set cannot form a triangle.

3. Set {5, 14, 19}

   • $5+14=19$ (not greater than)
   • Since the first condition fails, this set cannot form a triangle.

4. Set {9, 23, 33}

   • $9+23=32<33$ (False)
   • Since the first condition fails, this set cannot form a triangle.

In conclusion, the only set that can represent the sides of a triangle is:

{15, 25, 39}.