The inside perimeter of a running track (showninFig.15.67) 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.
Given,
Inside perimeter of track = 400m
Length of straight portion = 90m
Width of path = 14m
Total length of straight path = 90+90 = 180m
Remaining length = 400 – 180 = 220m
This length includes two semi circles or a complete circle.
So,
2πr = 220m
Then,
Area of path = (area of rectangles ABCD + rectangle EFGH + two semicircles)
= 14×90+14×90+π [(25+14)2 – 352]
[(a2 – b2) = (a+b)(a-b)]
Area of path = 6216m2
Length of outer track = 90+90+2πr
r = 35+14 = 49
= 180 +308 = 488m2
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