A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) If the perimeter of the window is 20 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) If the perimeter of the window is 20 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Tutorial Exercise
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to
the width of the rectangle, labeled x.)
If the perimeter of the window is 20 feet, find the exact value of x (in ft) so that the greatest possible amount of light is
admitted.
Step 1
X
Let x be the width (in ft) and y be the height (in ft) of the window. Thus, the semi-circle has radius We must maximize the
2
area of the window, A = xy + -
y =
Submit
-
X
π
2
플(슬)?
2 2
y
TTX
. The perimeter of the window is 20 = 2y + x + π
T(\-),
2
Skip (you cannot come back)
and so
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