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EAMCET Engineering 2005 Solved Paper
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© examsnet.com
Question : 113
Total: 160
Two sides of a triangle are given by the roots of the equation
x
2
−
5
x
+
6
=
0
and the angle between the sides is
π
3
. Then, the perimeter of the triangle is
5
+
√
2
5
+
√
3
5
+
√
5
5
+
√
7
Validate
Solution:
Given equation is
x
2
−
5
x
+
6
=
0
⇒
(
x
−
3
)
(
x
−
2
)
=
0
⇒
x
=
3
,
2
These are the sides of a triangle
Let
a
=
3
,
b
=
2
,
∠
C
=
π
3
∴
cos
C
=
a
2
+
b
2
−
c
2
2
a
b
⇒
cos
(
π
3
)
=
3
2
+
2
2
−
c
2
2.3
.2
⇒
1
2
=
13
−
c
2
12
⇒
c
2
=
13
−
6
=
7
⇒
c
=
±
√
7
⇒
c
=
√
7
(neglect
−
ve sign)
Perimeter of a triangle
=
a
+
b
+
c
=
3
+
2
+
√
7
=
5
+
√
7
© examsnet.com
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