A window is in the shape of a rectangle surmounted by a semicircle. If the perimeter of the
window is 20ft, then find the maximum area.
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Answer:
Clearly, r=2l
Perimeter =P(rectangle )+ P(semi-circle)
=2(l+b)+πr
=r+2b+πr=20
⇒b=220−r(1+π)
Area, A=lb+πr2
=2rb+πr2
=2r(20−r−rπ)+πr2=20r−r2
⇒drdA=20−2r=0 at r=10 dr2d2A=−2<0⇒ Maxima
⇒Amax=200−100=100 ft2
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