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JEE Main Math Class 11 Sequences and Series Part 3 Questions
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© examsnet.com
Question : 11
Total: 101
Let
ABC
be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle
ABC
and the same process is repeated infinitely many times. If
P
is the sum of perimeters and
Q
is be the sum of areas of all the triangles formed in this process, then:
[6 Apr 2024 Shift 2]
P
2
=
36
√
3
Q
P
2
=
6
√
3
Q
P
=
36
√
3
Q
2
P
2
=
72
√
3
Q
Validate
Solution:
👈: Video Solution
Area of first
∆
=
√
3
a
2
4
Area of second
∆
=
√
3
a
2
4
a
2
4
=
√
3
a
2
16
Area of third
∆
=
√
3
a
2
64
sum of area
=
√
3
a
2
4
(
1
+
1
4
+
1
16
.
.
.
)
Q
=
√
3
a
2
4
1
3
4
=
a
2
√
3
perimeter of
1
st
∆
=
3
a
perimeter of
2
nd
∆
=
3
a
2
perimeter of
3
rd
∆
=
3
a
4
P
=
3
a
(
1
+
1
2
+
1
4
+
.
.
.
)
P
=
3
a
⋅
2
=
6
a
a
=
P
6
Q
=
1
√
3
⋅
P
2
36
P
2
=
36
√
3
Q
© examsnet.com
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