Question Which of the following sets of numbers could represent the three sides of a triangle? Answer \[ \begin{array}{l}\{5,20,25\} \\ \{6,12,15\}\end{array} \] Submit Answer Whas \( \{7,21,27\} \)

The sets of numbers that can form a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. For the first set \{5, 20, 25\}, 5 + 20 is not greater than 25, so this cannot form a triangle. However, the second set \{6, 12, 15\} does satisfy the triangle condition: 6 + 12 > 15, 6 + 15 > 12, and 12 + 15 > 6. Therefore, it represents valid triangle side lengths. For the set \{7, 21, 27\}, checking the triangle inequalities shows that 7 + 21 is not greater than 27, leading us to conclude that this set also cannot form a triangle. So, only the set \{6, 12, 15\} truly qualifies as the sides of a triangle!