Question

Which set of numbers may be the lengths of the sides of a triangle?

A. {5, 4, 1}
B. {5, 4, 6}
C. {5, 4, 9}
D. {5, 4, 10}

Answer 1

To determine if a set of numbers can be the lengths of the sides of a triangle, we need to check if the sum of the lengths of any two sides is greater than the length of the third side. The sets {5, 4, 6} and {5, 4, 10} may be the lengths of the sides of a triangle.

Step-by-step explanation:

To determine if a set of numbers can be the lengths of the sides of a triangle, we need to check if the sum of the lengths of any two sides is greater than the length of the third side. Let's check each set of numbers:

1. {5, 4, 1}: The sum of the two smaller sides (1+4=5) is not greater than the longest side (5). This set cannot be the lengths of the sides of a triangle.
2. {5, 4, 6}: The sum of the two smaller sides (4+5=9) is greater than the longest side (6). This set can be the lengths of the sides of a triangle.
3. {5, 4, 9}: The sum of the two smaller sides (4+5=9) is equal to the longest side (9). This set cannot be the lengths of the sides of a triangle.
4. {5, 4, 10}: The sum of the two smaller sides (4+5=9) is smaller than the longest side (10). This set can be the lengths of the sides of a triangle.

Therefore, the sets that may be the lengths of the sides of a triangle are {5, 4, 6} and {5, 4, 10}.