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Byju's Answer
Standard VIII
Mathematics
Dilations
In figure, ...
Question
In figure,
D
E
∥
B
C
and
A
D
:
D
B
=
5
:
4
. Find
Area
(
A
D
E
)
Area
(
A
B
C
)
.
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Solution
∵
D
E
|
|
B
C
A
D
:
D
B
=
5
:
4
Δ
A
D
M
∼
Δ
A
B
N
∴
A
D
A
B
=
A
M
A
N
5
9
=
A
M
A
N
_____ (i)
∵
A
D
A
B
=
D
E
B
C
5
9
=
D
E
B
C
______ (ii)
a
r
(
Δ
A
D
E
)
=
1
2
×
D
E
×
A
M
______ (iii)
a
r
(
Δ
A
B
C
)
=
1
2
×
B
C
×
A
N
_______ (iv)
(iii) & (iv)
a
r
(
Δ
A
D
E
)
a
r
(
Δ
A
B
C
)
=
D
E
B
C
×
A
M
A
N
=
5
9
×
5
9
a
r
(
Δ
A
D
E
)
a
r
(
Δ
A
B
C
)
=
25
81
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