Test Index

BITSAT 2022 Paper

Section: Mathematics

© examsnet.com

Question : 101 of 130

Marks: +1, -0

A running track of

440\,\text{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

$70\,\text{ft}$ and $110\,\text{ft}$
$80\,\text{ft}$ and $120\,\text{ft}$
$35\,\text{ft}$ and $110\,\text{ft}$
$35\,\text{ft}$ and $120\,\text{ft}$

Solution: 👈: Video Solution

Perimeter

= 440

ft

\Rightarrow 2x + \pi r + \pi r = 440

2x + 2\pi r = 440

A =

Area of the rectangular portion

= x2r

A = \frac{x(440-2x)}{\pi} = \frac{1}{\pi}(440x-2x^2)

Let

\frac{dA}{dx} = \frac{1}{\pi}(440-4x)=0

\Rightarrow x=110

for which

\frac{d^2A}{dx^2} < 0

\Rightarrow A

is maximum when

x=110

\Rightarrow 2r = \frac{440-2x}{\pi} = \frac{440-220}{\frac{22}{7}} = 70

\therefore r=35

ft and

x=110

ft

© examsnet.com

Go to Question:

Prev Question

Next Question