A Norman window of maximum area can be constructed by adjoining a semicircle to the top of an ordinary rectangular window. The dimensions of the Norman window would be such that the radius is x/2 and the total perimeter is 22 feet.

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Let represent the measure of the vertical dimension of the rectangular portion of the window. Let represent the horizontal dimension of the window. is also the diameter of the semi-circular part of the window. The perimeter of the window is then: 22=x+2y+12πx PTotal=(PRectangle−x)+PCircle2 10−12x−15πx=y A=xy+π(12x)22 ATotal=ARetangle+ACircle2 A=x(10−12x−15πx)+π(12x)22 Plug in 10−12x−15πx for y A=10x−12x2−πx210 dAdX=10−x−πx5 Power rule ddxxn=nxn−1 0=10−x−πx5 Set dAdx equal to 0 x+πx5=10 Add x+πx5 to get x alone x(1+π5)=10 x=101+π5 x=404+π d2Adx2=−(4+π)4&amp;lt;0 Solve for y: y=10−(2+π)x4 Hence x=404+π is the x-coordinate of the maximum point. The y dimensoin and the semi-circle redius are calculated as above.

A Norman window is constructed by adjoining a semicircle to

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