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CDS Model Paper 1 Mathematics
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© examsnet.com
Question : 96
Total: 100
From a point in the interior of an equilateral triangle the perpendicular distances of the sides are
√
3
cm
,
2
√
3
cm
and
5
√
3
cm
. The perimeter (in
cm
) of the triangle is
64
32
48
24
Validate
Solution:
Let
ABC
be an equilateral triangle of side
x
cm
.
also, Let
OD
=
√
3
cm
,
OE
=
2
√
3
cm
and
OF
=
5
√
3
cm
From the figure,
ar
Δ
BOC
+
ar
Δ
AOC
+
ar
Δ
AOB
=
ar
Δ
ABC
or,
1
2
×
x
×
√
3
+
1
2
×
x
×
2
√
3
+
1
2
×
x
×
5
√
3
=
√
3
4
x
2
or,
2
√
3
+
4
√
3
+
10
√
3
=
√
3
x
or,
x
=
2
+
4
+
10
=
16
∴ Perimeter of the triangle
=
3
x
=
3
×
16
=
48
cm
© examsnet.com
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