The inside perimeter of a running track (shown in figure) is 400m. The length of each of the straight portion is 90m and the ends are semi-circles. If the track is everywhere 14m wide, find the area of the track. Also find the length of the outer running track.

Answer

`6216m^(2),488m`

Explanation

`90+90+2pir=400implies2xx22/7xx4r=220impliesr=35m`
So, `R=(35+14)m=49m`
Area of the track `=[(90xx14)+22/7xx{(49)^(2)-(35)^(2)}]m^(2)=6216m^(2)`
Length of the outer boundary `=(90+90+2piR)m`, where `R=49m`
`=488m`