Question

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

O {9,12,21}
O {9, 16, 27}
O {9, 24, 35}
O {7, 10, 14}

Answer 1

To determine if a set of numbers could represent the sides of a triangle, we need to check if the sum of the lengths of the two smaller sides is greater than the length of the longest side. {9, 16, 27} and {9, 24, 35} could represent the three sides of a triangle, while {9, 12, 21} and {7, 10, 14} could not.

Step-by-step explanation:

To determine if a set of numbers could represent the three sides of a triangle, we need to check if the sum of the lengths of the two smaller sides is greater than the length of the longest side. Let's calculate for each set:

1. {9, 12, 21}
2. The sum of the two smaller sides is 9 + 12 = 21, which is not greater than 21 (the longest side). Therefore, this set cannot represent the sides of a triangle.
3. {9, 16, 27}
4. The sum of the two smaller sides is 9 + 16 = 25, which is greater than 27 (the longest side). Therefore, this set can represent the sides of a triangle.
5. {9, 24, 35}
6. The sum of the two smaller sides is 9 + 24 = 33, which is greater than 35 (the longest side). Therefore, this set can represent the sides of a triangle.
7. {7, 10, 14}
8. The sum of the two smaller sides is 7 + 10 = 17, which is greater than 14 (the longest side). Therefore, this set can represent the sides of a triangle.