When a triangle is translated, the lengths of its sides do not change. The translation affects the position of the triangle but not the dimensions.
Since triangle XYZ is translated down 4 units and to the left 'a' units (where 'a' is the unspecified distance), the new triangle, which we'll denote as X'Y'Z', will still have sides of the same length as triangle XYZ.
Therefore, the length of side X'Y' remains the same as the length of side XY, which is 10 units.
So, the length of side X'Y' is 10 units.