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Standard X
Mathematics
Question
In the following, figure, seg DE || side BC in
△
A
B
C
. If
3
A
(
△
A
D
E
)
=
A
(
D
E
C
B
)
,
then find the ratio
B
C
:
D
E
?
1 : 2
16 : 1
2 : 1
1 : 16
A
16 : 1
B
1 : 16
C
2 : 1
D
1 : 2
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Solution
Verified by Toppr
3
A
(
△
A
D
E
)
=
A
(
D
E
C
B
)
⟹
A
(
△
A
B
C
)
=
4
A
(
△
A
D
E
)
⟹
A
(
△
A
B
C
)
A
(
△
A
D
E
)
=
4
In
△
A
D
E
and
△
A
B
C
,
∠
D
A
E
=
∠
B
A
C
D
E
∥
B
C
,
∠
A
D
E
=
∠
A
B
C
and
∠
A
E
D
=
∠
A
C
B
⟹
△
A
B
C
and
△
A
D
E
are similar.
⟹
A
(
△
A
B
C
)
A
(
△
A
D
E
)
=
(
B
C
D
E
)
2
⟹
4
=
(
B
C
D
E
)
2
⟹
B
C
D
E
=
2
1
Hence, option D is correct.
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Similar Questions
Q1
In the following, figure, seg DE || side BC in
△
A
B
C
. If
3
A
(
△
A
D
E
)
=
A
(
D
E
C
B
)
,
then find the ratio
B
C
:
D
E
?
View Solution
Q2
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a
n
d
s
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T
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A
(
△
A
B
C
)
A
(
△
P
B
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)
.
View Solution
Q3
In
△
ABC
,
seg
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∥
side
BC
.
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2
A
△
ADE
=
A
(
□
DBCE
)
,
f
ind
AB
:
AD
and
show
that
BC
=
3
×
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.