Asked by tom
Determine the maximum area of a piece of land comprising a semi-circle adjacent to a rectangle that can be enclosed by 850 metres of fencing.
Answers
Answered by
Damon
A = (1/2) pi r^2 + 2 r w
perimeter = 2 r + 2 w + 2 pi r = 850
= 2 r(1+pi) + 2 w
425 = r(4.14) + 2 w
213 = 2.07 r + w
w = (213 - 2.07 r)
A = .5 pi r^2 + 2r(213 - 2.07r)
A = 1.57 r^2 + 425 r - 4.14 r^2
2.57 r^2 -425 r = -A
r^2 - 165 r = -A/2.57
r^2 - 165 r + 6806 = -A/2.57 + 6806
(r-82.5) = -(1/2.57)( A - 17,492)
so I get
r = 2.5
and
area = 17,492
perimeter = 2 r + 2 w + 2 pi r = 850
= 2 r(1+pi) + 2 w
425 = r(4.14) + 2 w
213 = 2.07 r + w
w = (213 - 2.07 r)
A = .5 pi r^2 + 2r(213 - 2.07r)
A = 1.57 r^2 + 425 r - 4.14 r^2
2.57 r^2 -425 r = -A
r^2 - 165 r = -A/2.57
r^2 - 165 r + 6806 = -A/2.57 + 6806
(r-82.5) = -(1/2.57)( A - 17,492)
so I get
r = 2.5
and
area = 17,492
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