Question

Which side lengths allow you to construct a triangle?

A) 7, 2, and 2
B) 2, 3, and 8
C) 6, 8, and 10
D) 4, 1, and 9

Answer 1

To construct a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Among the given options, the side lengths 6, 8, and 10 (option C) allow us to construct a triangle.

Step-by-step explanation:

To construct a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let's go through the given side lengths:

1. A) 7, 2, and 2: The sum of the two shorter sides is 2 + 2 = 4, which is less than the longest side of 7. This combination cannot form a triangle.
2. B) 2, 3, and 8: The sum of the two shorter sides is 2 + 3 = 5, which is less than the longest side of 8. This combination cannot form a triangle.
3. C) 6, 8, and 10: The sum of the two shorter sides is 6 + 8 = 14, which is greater than the longest side of 10. This combination can form a triangle.
4. D) 4, 1, and 9: The sum of the two shorter sides is 4 + 1 = 5, which is less than the longest side of 9. This combination cannot form a triangle.

Therefore, the side lengths that allow us to construct a triangle are 6, 8, and 10 (option C).