### Home > PC > Chapter 6 > Lesson 6.4.1 > Problem 6-146

6-146.

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 running track. Let

*A*be the area of the rectangular region. Label all parts of the diagram. Note that*x*is the radius of the circular portion. Homework Help ✎Solve for

*y*in terms of*x*.Express

*A*as a function of*x*.

Circumference = 2*πr* (or 2*πx* in this case)

200 = 2*y* + 2*πx*

Use the information from part (a).

*A* = *xy* + *πx*^{2}