Answer
(a) $A(x)=-\frac{\pi+4}{8}x^2+15x$
(b) $x\approx8.4ft$, height $\approx4.2ft$
Work Step by Step
(a) The perimeter is the sum of the semicircle and three sides of the rectangular frame,
so the length of the height of the rectangular is $(30-\frac{\pi x}{2}-x)/2$, and the area
of the window is $A=x(30-\frac{\pi x}{2}-x)/2+\frac{\pi (x/2)^2}{2}=-\frac{\pi+4}{8}x^2+15x$
(b) As shown in the graph, the maximum of the window area happens when $x\approx8.4ft$
and the height would be $4.2ft$