To determine which side of triangle $\triangle XYZ$ is the longest, we need to use the relationship between the angles and the sides of a triangle. In any triangle, the side opposite the largest angle will be the longest side.

From the given image:

• $\angle X = 62^\circ$
• $\angle Y = 55^\circ$
• $\angle Z = 63^\circ$

Since $\angle Z = 63^\circ$ is the largest angle, the side opposite $Z$, which is $XY$, must be the longest side.

Therefore, the correct answer is A. $XY$.

Would you like further explanation or details on this?

Here are some related questions:

1. How can you use the Law of Sines to verify this?
2. What would happen if two angles were equal in a triangle?
3. How do the internal angles of a triangle always sum up?
4. What is the significance of an isosceles triangle in determining side lengths?
5. How does the Law of Cosines differ from using angle-side relationships?

Tip: Always remember, in any triangle, the side opposite the largest angle is the longest.