Mathematics

Problem

Triangles ABC and DEF are similar. It is known that

AB = 6\,\text{cm}

and

DE = 9\,\text{cm}

. The area of

\triangle DEF

180\,\text{cm}^2

. a. (i) Find the scale factor from

\triangle ABC

\triangle DEF

. b. (ii) Determine the area of

\triangle ABC

. c. (iii) If the altitude drawn from vertex A to side BC measures

4\,\text{cm}

, calculate the corresponding altitude drawn from vertex D to side EF.