Question

t
48 A window is in the shape of a rectangle
Sorrounded by a semiciacle . If the Perimeter
of the window is
window is 20ff, find
2off, find the maxima
area :​

Answer 1

Step-by-step explanation:

Clearly, r=

2

l

Perimeter =P(rectangle )+ P(semi-circle)

=2(l+b)+πr

=r+2b+πr=20

⇒b=

2

20−r(1+π)

Area, A=lb+πr

2

=2rb+πr

2

=2r(20−r−rπ)+πr

2

=20r−r

2

⇒

dr

dA

=20−2r=0 at r=10

dr

2

d

2

A

=−2<0⇒ Maxima

⇒A

max

=200−100=100 ft

2