Triangle ABC is right-angled at B, with AB = 9 cm and BC = 12 cm. On the extension of AC beyond C, a point D is taken such that ∠BCD=90∘ and CD = 8 cm.
a. (i) Find the length AC.
b. (ii) Calculate the length BD.
c. (iii) Determine the length AD.
d. (iv) Find the perimeter of quadrilateral ABCD.