Final answer:
Without additional information about the type of triangle, we can only order the side lengths given by their values as 57 < 60 < 63. If it's a right triangle, the Pythagorean theorem would confirm this order with 63 being the hypotenuse.
Step-by-step explanation:
The question relates to the concept of ordering the side lengths of a triangle. When ordering side lengths from shortest to longest, it is not stated whether the triangle is a right triangle or not. If it is a right triangle, the Pythagorean theorem can be applied. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In this case, if the given triangle is right-angled and the side lengths are 57, 63, and 60, then we would calculate 572 = 3249, 632 = 3969, and 602 = 3600. Since the longest side in a right triangle (the hypotenuse) has the largest value when squared, we can see that 3969 is the largest, indicating that the side with a length of 63 is the hypotenuse and thus the longest. The second longest side would be 60 and the shortest would be 57, ordered as 57 < 60 < 63. If it's not a right triangle, the information given is not sufficient to determine whether the sides obey the triangle inequality, but if they do, we would still order them in the same way based on their lengths as 57 < 60 < 63.