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Byju's Answer
Standard IX
Mathematics
Side Lengths
In figure , ...
Question
In figure ,
∠
M
N
P
=
90
o
,
s
e
g
N
Q
⊥
s
e
g
M
P
,
M
Q
=
9
cm ,
Q
P
=
4
cm, find
N
Q
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Solution
Area of
Δ
M
P
N
=
1
2
(
M
N
)
(
N
P
)
=
1
2
(
N
Q
)
(
M
P
)
∴
(
M
N
)
(
N
P
)
=
(
N
Q
)
=
(
M
P
)
∴
M
P
=
9
+
4
=
13
∴
M
N
2
+
N
P
2
=
169
∴
M
N
2
=
81
+
N
Q
2
∴
N
P
2
=
16
+
N
Q
2
∴
81
+
16
+
2
N
Q
2
=
169
∴
N
Q
2
=
169
−
97
2
∴
N
Q
2
=
36
∴
N
Q
=
6
cm.
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Similar questions
Q.
In the given figure, ∠MNP = 90°, seg NQ ⊥seg MP, MQ = 9, QP = 4, find NQ.