Solved: Geometry An indoor physical fitness room consists

Chapter , Problem 3.1.82

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Geometry An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a 200-meter single-lane running track. (a) Draw a diagram that gives a visual representation of the problem. Let and represent the length and width of the rectangular region, respectively. (b) Determine the radius of each semicircular end of the room. Determine the distance, in terms of around the inside edge of each semicircular part of the track. (c) Use the result of part (b) to write an equation, in terms of and for the distance traveled in one lap around the track. Solve for (d) Use the result of part (c) to write the area of the rectangular region as a function of What dimensions will produce a rectangle of maximum area?

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