Question

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.​

Answer 1

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

Step-by-step explanation:

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