Two triangles are similar. Their perimeters are 42 cm and 60 cm respectively. A side of the smaller triangle measures 12 cm, and the corresponding altitude in the larger triangle is 25 cm.
(i) Determine the scale factor between the triangles.
(ii) Calculate the length of the side in the larger triangle that corresponds to the 12 cm side.
(iii) Find the area of each triangle.
(iv) Prove that the ratio of the areas of the two triangles is equal to the square of the ratio of their perimeters.