Norman Window Is Constructed by Adjoining a Semicircle to the Top

Multiple Choice

Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure) . Find the dimensions of a Norman window of maximum area if the Total perimeter is 38 feet.

A) $x = \frac { 76 } { 2 + \pi }$ feet; $y = \frac { 38 } { 2 + \pi }$ feet
B) $x = \frac { 114 } { 2 + \pi }$ feet; $y = \frac { 38 } { 2 + \pi }$ feet
C) $x = \frac { 38 } { 4 + \pi }$ feet; $y = \frac { 76 } { 4 + \pi }$ feet
D) $x = \frac { 76 } { 4 + \pi }$ feet; $y = \frac { 38 } { 4 + \pi }$ feet
E) $x = \frac { 38 } { 4 + \pi }$ feet; $y = \frac { 114 } { 4 + \pi }$ feet