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CAT 2020 Exam Shift 2 Solved Paper
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© examsnet.com
Question : 51
Total: 76
The sum of the perimeters of an equilateral triangle and a rectangle is
90
c
m
. The area,
T
, of the triangle and the area,
R
, of the rectangle, both in sq
c
m
, satisfy the relationship
R
=
T
2
. If the sides of the rectangle are in the ratio
1
:
3
, then the length, in
c
m
, of the longer side of the rectangle, is
24
27
21
18
Validate
Solution:
Let the breadth of the rectangle be
b
.
Length of the rectangle
=
3
b
Let a be the side of the equilateral triangle.
Given,
R
=
T
2
⇒
3
b
2
=
(
√
3
4
×
a
2
)
2
⇒
b
=
a
2
/
4
Given,
2
(
4
b
)
+
3
a
=
90
⇒
8
(
a
2
/
4
)
+
3
a
−
90
=
0
⇒
2
a
2
+
3
a
−
90
=
0
⇒
(
a
−
6
)
(
2
a
+
15
)
=
0
⇒
a
=
6
∴
b
=
9
⇒
3
b
=
27
© examsnet.com
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