Question

A running track 440 ft. is to be laid out enclosing foot ball field which is in the shape a rectangle with a semi-circle at each end. If the area of the rectangular position is to be maximum then the dimensions of the rectangle are

• A. 100, 70
• B. 110, 70
• C. 100, 80
• D. 110, 60

Answer 1

Answer: (B)

110, 70

Perimeter of track $=2b+\pi a$
Area of rectangle $=ab$
$area=\frac{(440-2b)b}{\pi }$
$\frac{d\left(area\right)}{db}=440-2b-2b$
$0=440-4b$
$b=110$ $a=70$