Mathematics

Mathematics

Problem

In

\triangle ABC

,

AB = 15\,\text{cm}

,

AC = 18\,\text{cm}

and

BC = 20\,\text{cm}

. A point

D

is taken on

AB

such that

AD = 6\,\text{cm}

. The line through

D

drawn parallel to

BC

meets

AC

at

E

, and the line through

D

drawn parallel to

AC

meets

BC

at

M

. (i) Calculate

AE

and

EC

. (ii) Find the length

BM

. (iii) Determine the ratio of the areas of

\triangle ADE

and

\triangle ABC

.

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