1. ## geometry length

see attatched pic
the diagram shows a running track with the 'straights' 90m ling and with semicircular end sections.if the inside distance is 400m and the track is 8m wide, how much further is it to run around the outside of the track?

2. Originally Posted by mrmann
see attatched pic
the diagram shows a running track with the 'straights' 90m ling and with semicircular end sections.if the inside distance is 400m and the track is 8m wide, how much further is it to run around the outside of the track?
Where are the "straights" in the diagram? The diagram as posted shows two "concentric" ellipses only.

Anyway, I understand what you mean because we constructed a few of those ovals before.

The inside track:
(Assumed to be the innermost of the oval for this exercise)
Perimmeter, P1 = 400m
P1 = (two semicircles) +2(90) = 400
two semicircles = 400 -180 = 220
one circle = 220 m in circumference
radius, r = 220 / 2pi = 110/pi meters.

The outdside track:
(assumed also to be the outermost of the oval for this exercise.)
radius, R = r +8 = (110/pi0 +8
So,
Perimeter, P2 = (two semicircles) +2(90)
P2 = one circle +180
P2 = 2pi[(110/pi) +8] +180
P2 = 220 +16pi +180
P2 = 400 +16pi meters

So, P2 -P1 = (400 +16pi) -400 = 16pi
Meaning, it takes 16pi meters more to run around the outside track.
In decimals, that is 50.27 meters more.