Mathematics

Problem

In right-angled

\triangle ABC

(right angle at B), the altitude BD is drawn to the hypotenuse AC. a. (i) Prove that

\triangle ABD,\; \triangle CBD

and

\triangle ABC

are pairwise similar. b. (ii) Using the result of part (i), show that

BD^2 = AD \times DC.

c. (iii) If

AB = 15\,\text{cm}

and

BC = 20\,\text{cm},

calculate the lengths of BD, AD and DC.