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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
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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
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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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