field of Budhia has been actually divided into three
parts of equal area?
[Remark: Note that by taking
, the
triangle
ABC
is divided into three triangles
ABD
,
ADE
and
AEC
of equal areas. In the same way, by
dividing
BC
into
n
equal parts and joining the points
of division so obtained to the opposite vertex of
BC
, you can divide
into
n
triangles of equal
areas.]
Solution:
We are given that
We need to proof that
ar ABD ar ADE ar AEC .
Since
,
D
is the midpoint of
BE
in
.
So,
AD
is the median of
.
Thus,
... ( )ar ABD ar ADE i
(Since median of
a triangle divides it into two triangles of equal area)
Similarly,
AE
is the median of
(Since
is given)
Thus,
... ( )ar ADE ar AEC ii
(Since median of
a triangle divides it into two triangles of equal area)
From (i) and (ii), we have