Final answer:
Yes, it is possible to construct a triangle with the side lengths 28, 34, and 39. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, and all three combinations of two sides in this case satisfy the theorem.
Step-by-step explanation:
Yes, it is possible to construct a triangle with the side lengths 28, 34, and 39.
To determine if a triangle can be constructed, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let's check all three combinations of two sides:
28 + 34 = 62 > 39 - Yes, the sum is greater than 39.
28 + 39 = 67 > 34 - Yes, the sum is greater than 34.
34 + 39 = 73 > 28 - Yes, the sum is greater than 28.
Since all three combinations satisfy the triangle inequality theorem, it is possible to construct a triangle with side lengths 28, 34, and 39.