In ΔABC, points D and E lie on sides AB and AC respectively such that DE ∥ BC. It is given that AD = 2.5 cm, DB = 5 cm and AC = 18 cm.
a. (i) Prove that ΔADE is similar to ΔABC.
b. (ii) Find the lengths AE and EC.
c. (iii) Calculate the ratio of the areas of ΔADE and ΔABC.