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Byju's Answer
Standard X
Mathematics
SAS Similarity
In ABC, ∠ A...
Question
In
△
A
B
C
,
∠
A
B
C
=
90
o
,
B
M
⊥
A
C
,
B
M
=
x
+
2
,
A
M
=
x
+
7
,
C
M
=
x
, find
x
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Solution
It is given that
∠
A
B
C
=
90
0
and
B
M
⊥
A
C
as shown in the above figure:
Now with
B
M
=
(
x
+
2
)
,
C
M
=
x
and
A
M
=
(
x
+
7
)
, consider,
B
M
2
=
C
M
×
A
M
⇒
(
x
+
2
)
2
=
x
×
(
x
+
7
)
⇒
x
2
+
4
x
+
4
=
x
2
+
7
x
⇒
x
2
+
4
x
+
4
−
x
2
−
7
x
=
0
⇒
−
3
x
+
4
=
0
⇒
−
3
x
=
−
4
⇒
x
=
4
3
Hence,
x
=
4
3
.
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Similar questions
Q.
In
Δ
ABC, m
∠
B
=
90
,
¯
¯¯¯¯¯¯¯¯
¯
B
M
⊥
¯
¯¯¯¯¯¯
¯
A
C
,
M
∈
¯
¯¯¯¯¯¯
¯
A
C
. If AM
−
MC
=
7
,
A
B
2
−
B
C
2
=
175
. Find AC.
Q.
In
△
A
B
C
,
∠
A
B
C
=
90
o
and BM is the altitude. If AM = 16 MC Prove that
AB
=
4
BC
Q.
In triangle
A
B
C
measure is
∠
B
=
90
and
B
M
is an altitude if
A
M
=
B
M
=
8
.Then find AC
Q.
In
△
A
B
C
,
m
∠
B
=
90
o
,
¯
¯¯¯¯¯¯¯¯
¯
B
M
⊥
¯
¯¯¯¯¯¯
¯
A
C
,
M
∈
A
C
. If
A
M
−
M
C
=
7
and
A
B
2
−
B
C
2
=
175
, then find
A
C
.
Q.
In
Δ
A
B
C
;
B
M
⊥
A
C
and
C
N
⊥
A
B
;
Then,
A
B
A
C
=
B
M
C
N
=
A
M
A
N
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