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UPSC CDS Math Area and Perimeter Questions
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© examsnet.com
Question : 67
Total: 116
What is the area of a triangle with sides of length 12 cm, 13 cm and 5 cm ?
[2016 CDS-II]
30
c
m
2
35
c
m
2
40
c
m
2
42
c
m
2
Validate
Solution:
12
2
+
5
2
=
144
+
25
=
169
=
13
2
So, the sides 12 cm, 13 cm and 5 cm are the sides of a right triangle whose hypotenuse is 13 cm.
∴ Area of the triangle
=
1
2
×
12
×
5
=
30
c
m
2
Alternative method:
Here
s
=
a
+
b
+
c
2
=
12
+
13
+
5
2
=
15
c
m
∴ Area
√
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
=
√
15
(
15
−
12
)
(
15
−
13
)
(
15
−
5
)
=
√
15
×
3
×
2
×
10
=
√
900
=
30
c
m
2
© examsnet.com
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