Mathematics

Problem

\triangle ABC

and

\triangle DEF

are similar. The altitude from

A

BC

measures

4.5\,\text{cm}

and the corresponding altitude from

D

EF

measures

6\,\text{cm}

. If

BC = 7.5\,\text{cm}

and

AB = 6\,\text{cm}

, answer the following: a. (i) Find the ratio of the sides of

\triangle DEF

to those of

\triangle ABC

. b. (ii) Calculate the length of

EF

. c. (iii) Determine the length of

DE