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UPSC CDS Math Area and Perimeter Questions
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© examsnet.com
Question : 78
Total: 116
The base of an isosceles triangle is 300 units and each of its equal sides is 170 units. Then the area of the triangle is
[2016 CDS-I]
9600 square units
10000 square units
12000 square units
None of the above
Validate
Solution:
ΔABC is an isosceles triangle.
Draw AD ⊥ BC.
In an isosceles triangle, the perpendicular drawn to the base from the vertex opposite to the base bisects the base.
Therefore, D is the mid-point of BC.
⇒
B
D
=
D
C
=
300
2
=
150
units
In right ΔABD,
A
D
=
√
A
B
2
−
B
D
2
=
√
170
2
−
150
2
=
√
6400
=
80
units
Therefore, area of ΔABC
=
1
2
×
B
C
×
A
D
=
1
2
×
300
×
80
=
12
,
000
square units
© examsnet.com
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