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Wednesday, December 31, 2014

Circle and Rectangle Problems, 2

Category: Plane Geometry

"Published in Vacaville, California, USA"

A running track has the shape shown in the figure, with straight sides and semicircular ends. If the length of the track is 440 yd and the two straight parts are each 110 yd long, what is the radius of the semicircular parts (to the nearest yard)?

Photo by Math Principles in Everyday Life


Consider the given figure above 

Photo by Math Principles in Everyday Life

Since the middle part of the running track is a rectangle, then the diameters of the two semicircular parts are equal. The width of a rectangle is equal to the diameter of two semicircles. If we combine the length of two semicircles, then it becomes a length or circumference of a circle. Hence, the length of a running track is


Therefore, the radii of the semicircular parts of a running track are