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 find the lengths of its sides.

Explanation

perameter =440 ft.
`2x+pir+pir=440 "or" 2x+2pir=440`
A=Area of the rectangular portion =x2r
`=x(440-2x)/(pi)=(1)(pi)(440x-2x^(2))`
Let `(dA)/(dx)=(1)/(pi)(440-4x)=0`
Then,x =110 for which `(d^(2)A)/(dx^(2))lt0`
Thus ,A is maximum when x=110 . Therefore,
`2r=(440-2x)/(pi)=(440-220)(22//7)=70 M`
or r=35 ft and x=110 ft