The figure below depicts a racetrack with ends that are semicircular. The length of the track is 660 ft (1/8 mi). Find l and r so that the area of the rectangular portion of the region enclosed by the racetrack is as large as possible. (Round your answers to the nearest foot.)

Answer 1

2l + 2πr = 660
a = 2lr + πr^2
= 2(660-2πr)/2 * r + πr^2
= r(660-2πr) + πr^2
= 660r - πr^2

Now just set da/dr=0 to find r, then l.