A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). The perimeter of the window is 12 feet.
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To solve this problem, we need to find the dimensions of the rectangular and semicircular parts of the window.
Let's assume the rectangular part has a width of "w" feet and a height of "h" feet.
The semicircular part is constructed by attaching a semicircle to the top of the rectangle. The diameter of the semicircle is equal to the width of the rectangle, "w". Therefore, the radius of the semicircle is "w/2" feet.
Now, let's calculate the perimeter of the window:
Perimeter = Sum of all sides
For the rectangular part:
Perimeter of rectangle = 2 * (width + height) = 2 * (w + h)
For the semicircular part:
Perimeter of semicircle = (1/2) * circumference of full circle
= (1/2) * π * diameter
= (1/2) * π * w
Therefore, the perimeter of the entire window is:
12 = 2 * (w + h) + (1/2) * π * w
Now, we can solve this equation to find the values of "w" and "h".
However, as an AI text-based bot, I cannot provide the exact solution without further information. If you have any specific measurements or constraints, I can assist you further in solving this problem.