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Byju's Answer
Standard X
Mathematics
Relation between Areas and Sides of Similar Triangles
The medians ...
Question
The medians
B
E
and
C
F
of a
△
A
B
C
intersect at
G
. Prove that area (
△
G
B
C
)
a
r
=
□
A
F
G
E
.
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Solution
B
E
is the median of
Δ
A
B
C
so,
a
r
(
Δ
B
E
C
)
=
1
2
a
r
(
Δ
A
B
C
)
__(1)
Median of triangle divides into 2 triangles of equal area.
Also
C
F
is median of
Δ
A
B
C
⇒
a
r
(
Δ
A
C
F
)
=
1
2
a
r
(
Δ
A
B
C
)
__(2)
from (1) and (2)
a
r
(
Δ
A
C
F
)
=
a
r
(
Δ
B
E
C
)
a
r
(
Δ
G
B
C
)
+
a
r
(
Δ
G
E
C
)
=
a
r
(
A
F
G
E
)
+
a
r
(
G
E
C
)
∴
a
r
(
Δ
G
B
C
)
=
a
r
(
A
F
G
E
)
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Standard X Mathematics
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