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There is  a figure (norman window) in which a rectangle is surmounted by a semicircle with diameter along one side of the rectangle .If the perimeter is given find the radius of the semicircle if the area is to be maximum (maximum amount of light is to be admitted into the room)


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 There is  a figure (norman window) in which a rectangle is surmounted by a semicircle with diameter along one side of the rectangle .If the perimeter is given find the radius of the semicircle if the area is to be maximum (maximum amount of light is to be admitted into the room)
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Write a expression for area and perimeter of the figure
perimeter is constant
use the expression of the perimeter to eliminate one of the variables (radius or side of the rectangle)
from the expression for area
diff. twice
equate the first derivative to zero  to find critical values
 answer and  some steps are given below
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