Final answer:
The ratio of corresponding sides of two similar triangles with perimeters of 12 cm and 24 cm, respectively, is 1:2.
Step-by-step explanation:
The student is asking about the ratio of corresponding sides of two similar triangles with perimeters of 12 cm and 24 cm, respectively. Since the triangles are similar, the sides are proportional, and the ratio of their corresponding sides will be the same as the ratio of their perimeters. Thus, if we take the ratio of the perimeters, 12 cm to 24 cm, we can reduce this to its simplest form of 1:2. This ratio of 1:2 gives us the ratio of the lengths of the corresponding sides of the two triangles. This core concept of similar figures applies in many areas of geometry and helps us understand the consistent relationships between the dimensions of shapes that have the same form.