Mathematics

Problem

\triangle ABC

AB = 9\,\text{cm}

and

AC = 15\,\text{cm}

. A point

D

is taken on

AB

such that

AD = 3\,\text{cm}

. A point

E

is taken on

AC

so that

DE

is parallel to

BC

. a. (i) Write the ratio

AD:DB

. b. (ii) Using the condition that

DE

is parallel to

BC

, calculate the length

AE

. c. (iii) Verify your answer by showing explicitly that the two required ratios are equal.