SOLUTION: A farmer wants to enclose two adjacent rectangular regions next to a river, one sheep and one for cattle. No fencing is needed next to the river, but fencing must be used to divide
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Question 428258: A farmer wants to enclose two adjacent rectangular regions next to a river, one sheep and one for cattle. No fencing is needed next to the river, but fencing must be used to divide the sheep pen for the cattle pen. The farmer has 60 meters of fencing in all. What is the area of the largest region that can be enclosed? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A farmer wants to enclose two adjacent rectangular regions next to a river, one sheep and one for cattle. No fencing is needed next to the river, but fencing must be used to divide the sheep pen for the cattle pen. The farmer has 60 meters of fencing in all. What is the area of the largest region that can be enclosed?
:
From the information given, we will need 3 widths and 1 length
:
L + 3W = 60
L = (60-3W)
;
Area
A = L*W
Replace L with (60-3W)
A = W(60-3W)
A = -3W^2 + 60W
max area occurs at the axis of symmetry, (x=-b/(2a)), in this equation a=-3, b=60
W =
W = + 10 meters is the width
Find the Length
60 - 3(10) = 30 meters is the length
:
Max area: 30 * 10 = 300 sq/meters
