A running track of 440 m is to be laid out enclosing a football field, the shape of which is a rectangle with semi circle at two opposite end. If the area of the rectangular portion is to be maximum, then the length of its sides is

Question

A running track of 440 m is to be laid out enclosing a football field, the shape of which is a rectangle with semi circle at two opposite end. If the area of the rectangular portion is to be maximum, then the length of its sides is (A) 120 m , (220/π) m (B) 110 m , (π/200) m (C) 110 m , (220/π) m (D) 125 m , (220/π) m

Tardigrade Admin · Accepted Answer

2 ℓ+2 π r=440 A =ℓ 2 r=-2 π r2+440 r ( dA / dr )=-4 π r +440=0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f48d8224c550010224f4cfa151254dfd-.png" /> at r =110 m , (220/π) m

Q. A running track of $440 m$ is to be laid out enclosing a football field, the shape of which is a rectangle with semi circle at two opposite end. If the area of the rectangular portion is to be maximum, then the length of its sides is

$120 m, \frac{220}{π} m$

$110 m, \frac{π}{200} m$

$110 m, \frac{220}{π} m$

$125 m, \frac{220}{π} m$

$2 ℓ + 2 π r = 440$
$A = ℓ 2 r = - 2 π r^{2} + 440 r$
$\frac{d A}{d r} = - 4 π r + 440 = 0$

at $r = 110 m, \frac{220}{π} m$

Q. A running track of 440m is to be laid out enclosing a football field, the shape of which is a rectangle with semi circle at two opposite end. If the area of the rectangular portion is to be maximum, then the length of its sides is

120m,π220​m

110m,200π​m

110m,π220​m

125m,π220​m