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A window is in the form of a r...

# A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

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Solution : 2a + b + pi b/2 = 10 <br> a = (10 - b - pi b/2)/2 <br> area = ab + pi/2*b^2/4 <br> = ((10-b-pib/2)b)/2 + (pib^2)/8 <br> = 5b^ - b^2/2 - (pi b^2)/4 + (pib^2)/8 <br> = 5b - b^2/2 - (pib^2)/8 <br> (dA)/(db) = 0 <br> => 5-b- pi/4*b = 0 <br> b= 5/(1 + pi/4) <br> (d^2A)/(db^2) = 0-1-pi/4 <0  <br> a = (10-b-pi b/2)/2 = 10/(pi +4) <br> area = (20/(pi+4))(10/(pi+4)) + pi/2*400/(4(pi+4)^2) <br> = (200+50 pi)/(pi+4)^2 = 50/(pi+4) unit^2 <br> answer
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