Question 104187: A rectangular plot, bounded on one side by a river, is to be enclosed on the other 3 sides by a fence, and then divided into two equal sized pens by another fence. If you have 900 feet of fence available, what is the largest are that can be enclosed?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular plot, bounded on one side by a river, is to be enclosed on the other 3 sides by a fence, and then divided into two equal sized pens by another fence. If you have 900 feet of fence available, what is the largest are that can be enclosed?
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Perimeter would be:
L + 3W = 900
or
L = (900-3W)
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Area would be:
A = W * L
Substitute for L
A = W(900-3W)
A = -3W^2 + 900W
:
A quadratic, find the axis of symmetry using: x = -b/(2a); a = -3; b= 900
W = -900/(2*-3)
W = -900/-6
W = 150 ft is the width for max area
:
Find Max area, substitute 150 for W
A = -3(150^2) + 900(150)
A = -3(22500) + 135000
A = -67500 + 135000
A = +67500 sq ft is max area
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If you graph it: x = width, y = area
:
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Check it:
L = 900 - 3(150)
L = 900 - 450
L = 450 ft
So it would be 450 by 150: 450*150 = 67500 sq ft
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