Math
posted 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?

A = L * w
Perimeter = L + 2 w = 36
so
L = 362w
A = (362w)w
2 w^2 + 36 w = A
w^2  18 w = A/2
w^2  18 w + 81 = A/2 + 81
(w9)^2 = (1/2)(A162)
vertex at
w = 9
area = 162 ft^2
====================
check
if w = 9
L = 36  18 = 18
area = 162, sure enough
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