Greenwood press

PERIMETER
65
The area of a square pen with a perimeter
of 40 meters as a function of its width.
Equally divided rectangular pen
with length l and width w to
hold two different animals.

---

Marking the starting positions in different lanes uses principles of perimeter.
For example, suppose the width of each lane is 1.067 meters, and the inner radius
of the turn is 63.662 meters. In one lap around the track, the runner in lane 1
would run 400 meters, but the runners in the other lanes would run farther if they
all started in the same position and had to stay in their lanes. The runner in lane
2 would be running around a turn with a radius of 64.729 meters, which would 
make each turn 
64.729π
2
≈ 101
.676 meters. Therefore the runner in lane 2 should 
start a 400-meter race ahead of the runner in lane 1 by 1.676 meters around the
first turn. Since the lanes are of equal width, each runner in sequential lanes
should start 1.676 meters around the first turn ahead of the previous runner. In a
4
× 400 meter relay, the second runner can move into the first lane after his or
her first turn, which is the fifth turn overall. When staggering this relay, the run-
ner in lane 2 should be moved 50 percent ahead of the other arrangement, since
three of the turns will be run in the same lane instead of two. This means that
each lane should be staggered by (1.50)(1.676) = 2.514 meters apart in this race.
online sources for further exploration
Designing a track

Floor plans




Maximize the area of a rectangular field with fixed perimeter

Starting a new game farm

▲
▼
▲