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BITSAT 2022 Solved Question Paper
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© examsnet.com
Question : 101
Total: 130
A running track of
440
ft
is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then the lengths of its side are
70
ft
and
110
ft
80
ft
and
120
ft
35
ft
and
110
ft
35
ft
and
120
ft
Validate
Solution:
👈: Video Solution
Perimeter
=
440
ft
⇒
2
x
+
π
r
+
π
r
=
440
2
x
+
2
π
r
=
440
A
=
Area of the rectangular portion
=
x
2
r
A
=
x
(
440
−
2
x
)
π
=
1
π
(
440
x
−
2
x
2
)
Let
d
A
d
x
=
1
π
(
440
−
4
x
)
=
0
⇒
x
=
110
for which
d
2
A
d
x
2
<
0
⇒
A
is maximum when
x
=
110
⇒
2
r
=
440
−
2
x
π
=
440
−
220
22
7
=
70
∴
r
=
35
ft and
x
=
110
ft
© examsnet.com
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