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CDS Model Paper 5 Mathematics
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© examsnet.com
Question : 97
Total: 100
A
B
C
is an isosceles triangle right angled at B. Two equilateral triangles are constructed with side
B
C
and
A
C
as shown in figure. Find the ratio of
ar
(
Δ
B
C
D
)
and
ar
(
Δ
A
C
E
)
.
2
:
1
1
:
4
4
:
1
1
:
2
Validate
Solution:
Let the side right isoceles triangle
=
a unit Now,
Now,
In
Δ
B
C
D
[equilateral triangle]
Hight
=
√
3
2
a
Area
(
Δ
B
C
D
)
=
1
2
×
b
×
h
=
1
2
×
a
×
√
3
2
a
=
√
3
4
a
2
sq. unit. ...(i)
In equilateral
(
Δ
A
E
C
)
: -
Side
=
√
a
2
+
a
2
=
a
√
2
unit
Height
=
√
3
2
×
a
×
√
2
=
√
6
2
a
Area
(
Δ
A
E
C
)
=
1
2
×
b
×
h
=
1
2
×
a
√
2
×
√
6
2
a
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