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A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) 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?

The width of the window should be ft, and the height of the window should be ft.

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calculista calculista · Answer 1 · 2019-04-15T22:52:45+02:00

Answer:

The width of the window should be [tex]7.6\ ft[/tex] and the height of the window should be [tex]3.8\ ft[/tex]

Step-by-step explanation:

we know that

The circumference of a semicircle (window) is equal to

[tex]C=\pi r[/tex]

we have that

[tex]C=12\ ft[/tex]

[tex]\pi=3.14[/tex]

substitute and solve for r

[tex]12=(3.14)r[/tex]

[tex]r=12/3.14=3.8\ ft[/tex]

so

the width of the window is equal to the diameter of the semicircle

so

The width of the window should be [tex]3.8*2=7.6\ ft[/tex] and the height of the window should be [tex]3.8\ ft[/tex]