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UPSC CDS Math Triangles Questions
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© examsnet.com
Question : 5
Total: 68
ABC is a triangle right angled at B. If AB = 5 cm and B C = 10 cm, then what is the length of the perpendicular drawn from the vertex B to the hypotenuse ?
[2019 CDS-II]
4 cm
2
√
5
cm
4
√
5
cm
8 cm
Validate
Solution:
Given that ∆ABC is a right-angled triangle and
A
B
=
5
c
m
,
B
C
=
10
c
m
Then,
A
C
=
√
A
B
2
+
B
C
2
=
√
25
+
100
=
5
√
5
If BP is perpendicular on
A
C
,
the then are of the
∆
A
B
C
A
=
1
2
⋅
A
B
⋅
B
C
=
1
2
⋅
A
C
⋅
P
B
⇒
A
B
⋅
B
C
=
A
C
⋅
P
B
⇒
5
×
10
=
5
√
5
×
P
B
⇒
P
B
=
2
√
5
c
m
© examsnet.com
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