Question

A track and field playing area is in the shape of a rectangle with semicircles at each end. See the figure. The inside perimeter

Answer 1

Answer:

Step-by-step explanation:

Let x be the track straights lengths

Let y be the track ends diameter and the other rectangle side lengths.

1800 = 2x + πy

y = (1800 - 2x) / π

A = xy

A = x((1800 - 2x) / π

A = (1/π)(1800x - 2x²)

dA/dx = (1/π)(1800 - 4x)

       0 = (1/π)(1800 - 4x)

       0 = 1800 - 4x

     4x = 1800

        x = 450 m

        y = (1800 - 2(450)) / π

        y = 900/π or approximately 286.5 m