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SSC CGL Tier 2 Exam 21 Sep 2014 Paper
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© examsnet.com
Question : 14
Total: 100
a and b are two sides adjacent to the right angle of a rightangled triangle and p is the perpendicular drawn to the hypotenuse from the opposite vertex. Then
p
2
is equal to
a
2
+
b
2
1
a
2
+
1
b
2
a
2
b
2
a
2
+
b
2
a
2
−
b
2
Validate
Solution:
(3)
BD ⊥ AC
AB ⊥ BC
Hypotenuse of ΔABC
=
√
A
B
2
+
B
C
2
=
√
a
2
+
b
2
Area of
Δ
ABC
=
1
2
×
A
B
×
B
C
=
1
2
×
A
C
×
B
D
⇒
A
B
×
B
C
=
A
C
×
B
D
⇒
a
b
=
√
a
2
+
b
2
×
p
On squaring both sides,
a
2
b
2
=
(
a
2
+
b
2
)
p
2
∴
p
2
=
a
2
b
2
a
2
+
b
2
© examsnet.com
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