Asked by Kate
A farmer has 36 feet of fence to build a pigpen. He is going to use one of the sides of his barn as a side to the rectangular enclosure. Determine a function A that represents the total area of the enclosed region. What is the maximum area that can be enclosed?
Answers
Answered by
Damon
A = L * w
Perimeter = L + 2 w = 36
so
L = 36-2w
A = (36-2w)w
-2 w^2 + 36 w = A
w^2 - 18 w = -A/2
w^2 - 18 w + 81 = -A/2 + 81
(w-9)^2 = -(1/2)(A-162)
vertex at
w = 9
area = 162 ft^2
====================
check
if w = 9
L = 36 - 18 = 18
area = 162, sure enough
Perimeter = L + 2 w = 36
so
L = 36-2w
A = (36-2w)w
-2 w^2 + 36 w = A
w^2 - 18 w = -A/2
w^2 - 18 w + 81 = -A/2 + 81
(w-9)^2 = -(1/2)(A-162)
vertex at
w = 9
area = 162 ft^2
====================
check
if w = 9
L = 36 - 18 = 18
area = 162, sure enough
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