### Home > PC > Chapter 6 > Lesson 6.4.1 > Problem6-146

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.

1. Solve for $y$ in terms of $x$.

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

$200 = 2y + 2πx$

2. Express $A$ as a function of $x$.

Use the information from part (a).

$A = xy + πx^{2}$