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Byju's Answer
Standard X
Mathematics
AAA Similarity
In a Δ ABC,...
Question
In a
Δ
A
B
C
,
D
and
E
are points on the sides
A
B
and
A
C
respectively such that
D
E
|
|
B
C
.
If
A
D
=
8
x
−
7
,
D
B
=
5
x
−
3
,
A
E
=
4
x
−
3
and
E
C
=
(
3
x
−
1
)
, find the value of
x
.
Open in App
Solution
I
n
Δ
A
D
E
&
Δ
A
B
C
∠
A
=
∠
A
&
∠
A
D
E
=
∠
A
B
C
∴
Δ
A
D
E
∼
Δ
A
B
C
[
A
A
−
s
i
m
i
l
a
r
i
t
y
]
A
D
A
B
=
A
E
A
C
8
x
−
7
8
x
−
7
+
5
x
−
3
=
4
x
−
3
4
x
−
3
+
3
x
−
1
⇒
(
8
x
−
7
)
(
7
x
−
4
)
=
(
4
x
−
3
)
(
13
x
−
10
)
⇒
56
x
2
−
32
x
−
49
x
+
28
=
52
x
2
−
40
x
−
39
x
+
30
⇒
56
x
2
−
81
x
+
28
−
52
x
2
+
79
x
−
30
=
0
⇒
4
x
2
−
2
x
−
2
=
0
⇒
2
x
2
−
x
−
1
=
0
⇒
2
x
2
−
2
x
+
x
−
1
=
0
⇒
2
x
2
−
2
x
+
x
−
1
=
0
⇒
2
x
(
x
−
1
)
+
1
(
x
−
1
)
=
0
⇒
(
2
x
+
1
)
(
x
−
1
)
=
0
∴
2
x
+
1
=
0
a
n
d
x
−
1
=
0
∴
x
=
−
1
2
a
n
d
x
=
1
s
i
n
c
e
l
e
n
g
t
h
c
a
n
n
o
t
b
e
−
v
e
∴
x
=
1.
Suggest Corrections
0
Similar questions
Q.
In a
Δ
A
B
C
,
D
and
E
are points on the sides
A
B
and
A
C
respectively such that
D
E
|
|
B
C
.
If
A
D
=
4
x
−
3
,
A
E
=
8
x
−
7
,
B
D
=
3
x
−
1
and
C
E
=
5
x
−
3
, find the value of
x
.
Q.
In a
Δ
A
B
C
,
D
and
E
are points on the sides
A
B
and
A
C
respectively such that
D
E
|
|
B
C
.
If
A
D
=
4
,
A
E
=
8
,
D
B
=
x
−
4
, and
E
C
=
3
x
−
19
, find
x
.
Q.
In a
Δ
A
B
C
,
D
and
E
are points on the sides
A
B
and
A
C
respectively such that
D
E
|
|
B
C
.
If
A
D
=
x
,
D
B
=
x
−
2
,
A
E
=
x
+
2
and
E
C
=
x
−
1
, find the value of
x
.
Q.
In
△
ABC, D and E are points on the sides AB and AC respectively such that DE || BC.
If AD =
4
x
−
3
, BD =
3
x
−
1
, AE =
8
x
−
7
and CE =
5
x
−
3
find the value
x
.
Q.
In a
Δ
A
B
C
,
D
a
n
d
E
are points on the sides
A
B
and
A
C
respectively such that
D
E
∥
B
C
. If
A
D
=
4
x
−
3
,
A
E
=
8
x
−
7
,
B
D
=
3
x
−
1
a
n
d
C
E
=
5
x
−
3
, find the value of
x
.
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