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UPSC CDS 2 2018 Math Paper
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© examsnet.com
Question : 71
Total: 100
If base and hypotenuse of a right triangle are
(
u
2
−
v
2
)
and
(
u
2
+
v
2
)
respectively and the area of the triangle is 2016 square units, then the perimeter of the triangle may be
[2018 CDS-II]
224 units
288 units
448 units
576 units
Validate
Solution:
(
u
2
+
v
2
)
2
=
(
u
2
−
v
2
)
2
+
(
2
u
v
)
2
∴ Height of triangle = 2uv
1
2
×
2
u
v
(
u
2
−
v
2
)
=
2016
⇒
u
v
(
u
+
v
)
(
u
−
v
)
=
9
×
7
×
(
9
+
7
)
×
(
9
−
7
)
⇒
u
=
9
,
v
=
7
Hypotenuse
=
9
2
+
7
2
=
130
Base
=
9
2
–
7
2
=
32
Height
=
2
×
9
×
7
=
126
Perimeter of triangle
=
130
+
32
+
126
=
288
units.
© examsnet.com
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