In the given figure, DE is parallel to BC and D and E are the mid points of sides AB and AC respectively.

The ratio of the lengths of DE and BC is

DE is parallel to BC, and D and E are the midpoints of AB and AC respectively.

The length of the line joining the midpoints of two sides of a triangle is half of the length of the third side.

Hence, $DE=\frac{1}{2}BC$

Thus, the ratio of the lengths of DE and BC = 1:2.

Therefore, 1:2 is the correct response.