In , , and . A point is taken on such that . The line through drawn parallel to meets…

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

\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

E

, and the line through

D

drawn parallel to

AC

meets

BC

M

. (i) Calculate

AE

and

EC

. (ii) Find the length

BM

. (iii) Determine the ratio of the areas of

\triangle ADE

and

\triangle ABC