CPM Homework Help : PCT Problem 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.

Solve for $y$ in terms of $x$ .
Hint (a):
Circumference $= 2πr$ (or $2πx$ in this case)
Step (a):
$200 = 2y + 2πx$
Express $A$ as a function of $x$ .
Hint (b):
Use the information from part (a).
Step (b):
$A = xy + πx^{2}$

Horizontal rectangle, bottom edge labeled, y, with semi-circles, one on each right & left edge, with edge as the diameter, radius on right semicircle labeled, x.