Mathematics

Problem

\triangle ABC

, points

D

AB

and

E

AC

are chosen so that

DE

is parallel to

BC

. The lengths

AD = 3\,\text{cm}

DB = 5\,\text{cm}

and

AC = 12\,\text{cm}

are given. a. (i) Find the lengths of

AE

and

EC

. b. (ii) What percentage of

AC

AE

? Give your answer correct to the nearest whole percent.