In , points D and E are taken on AB and AC respectively such that and . Join DE.…

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

Problem

\Delta ABC

, points D and E are taken on AB and AC respectively such that

AD : DB = 1 : 2

and

AE : EC = 1 : 2

. Join DE. Further, points F and G are taken on AD and AE respectively so that

AF : FD = 1 : 2

and

AG : GE = 1 : 2

. Join FG. (i)

\Delta ADE

is similar to

\Delta ABC

and hence obtain the ratio of their areas. (ii)

\Delta AFG

is similar to

\Delta ADE

. (iii) Hence show that the area of

\Delta AFG

\frac{1}{81}

of the area of

\Delta ABC