A Norman window is a window with a semicircle on top of a regular rectangular window as shown in the diagram. What should the dimensions of the rectangular part of a Norman window be to allow in as much light as possible if there is only 12 ft of the framing material available?

The dimensions of the rectangular window that gives a maximum area are as follows;Width = [tex]\dfrac{12}{2+\pi }[/tex] feet and length = 3 feetWhat is the maximum value of a function?The maximum value of a function is given by the point at which the graph of the function has the highest value.The parameters of the window are;Length of the framing material available = 12 ft.The shape of the window = A semicircle on top of a regular rectangular windowRequired; The dimension of the rectangular part of the Norman window that allows the most light Solution;Diameter of the semicircular part of the window = The width of the rectangular partLet x represent the width of the window, we have;Perimeter of the semicircle = π·x/2Side length of the rectangular window = (12 - π·x/2 - x)/2Area of the rectangular part of the window, A = x × (12 - π·x/2 - x)/2Area of the semicircle = π·x²÷4Area of the window, is therefore;[tex]A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} +\dfrac{ \pi \cdot x^2}{4}[/tex]At the maximum area, of the rectangular part, we have;[tex]A_r' =\dfrac{d}{dx}\left( A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} \right) = -\dfrac{x\cdot \pi +2\cdot x-12}{2} = 0[/tex]x·π + 2·x - 12 = 0The width, x = [tex]\dfrac{12}{2+\pi }[/tex] feetThe length of the rectangle is therefore;[tex](12 - \pi \cdot \dfrac{6}{2+\pi } - \dfrac{12}{2+\pi })/2 = 6 - \pi \cdot \dfrac{3}{2+\pi } - \dfrac{6}{2+\pi } = 3[/tex]The length of the rectangular window = 3 feetLearn more about the maximum value of a function here:https://brainly.com/question/15300035#SPJ1