PLEASE HELP
A track and field playing area is in the shape of a rectangle with semicircles at each end. See the figure. The inside perimeter of the track is to be 1700 meters. What should the dimensions of the rectangle be so that the area of the rectangle is maximized?

What are the dimensions of the rectangle?

P = 1700= 82.47m  length x 20.61m depth

In ratio to the semi circles 16.4 x 4.1 = 64.9 circumference/

4/6 approx

Semi circles at each end = 2/6 approx

Circumference of a circle = C=2πr

= 6.28 x 20.61 = 129.4308     /2

Where each end 64.9 = 16.1 x 4.02= 64.72m^2 area approx if squared.

Then the measurement of the rectangle would have larger area 1828m^2  but as separate the rectangle length is 82.47m depth is 20.61 with 1700m^2.

Step-by-step explanation: