Question

A Norman window is a window with a semi-circle on top of regular rectangular window. What should be the dimensions of the window to allow in as much light as possible, if there are only 12 ft of the frame material available? Please find the height of the norman window

Answer 1

Answer:

1.68 ft

Step-by-step explanation:

Let x be the radius

Arc length = 3.14x

Width = 2x

Height = [12 - (2x) - 3.14x]/2

= 6 - 2.57x

Area = 3.14x²/2 + 2x(6 - 2.57x)

Area = 12x - 3.57x²

dA/dx = 12 - 7.14x = 0

x = 1.6806722689

Height = 6 - 2.57x

= 1.6806722689