Answer the following questions related to altitudes of similar triangles.
(i) State the relationship between the lengths of corresponding altitudes of two similar triangles.
(ii) In △ABC and △PQR, it is given that △ABC∼△PQR and the ratio of their corresponding sides is 5:8. Without performing any numerical calculation other than proportional reasoning, write the ratio of
(a) their areas,
(b) the altitudes drawn to their shortest sides. Give reasons for your answers.
(iii) Explain why the ratio obtained in part (ii)(b) must be equal to the given side ratio.