SOLUTION: A farmer plans to fence a rectangular grazing area along a river with 300 yards of fence. Write an expression for the area A of grazing land in terms of the width w of the rectangl
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Question 106355: A farmer plans to fence a rectangular grazing area along a river with 300 yards of fence. Write an expression for the area A of grazing land in terms of the width w of the rectangle. Also, what is the largest area he can enclose? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A farmer plans to fence a rectangular grazing area along a river with 300 yards of fence. Write an expression for the area A of grazing land in terms of the width w of the rectangle. Also, what is the largest area he can enclose?
:
Since one side is the river, the rectangle's fence perimeter will be:
L + 2W = 300
L = 300 - 2W
:
Area = Length * Width
Substitute (300-2W) for L:
A = W(300 - 2W)
A = -2W^2 + 300W; this would be the expression
:
This is a quadratic equation, Find the axis of symmetry, x = -b/(2a)
In our equation it would be:
W = -300/(2*-2)
W = -300/-4
W = +75 is the width for max area:
:
Find the max area, substitute 75 for W
A = -2(75^2) + 300(75)
A = -2(5625) + 22500
A = -11250 + 22500
A = 11250 sq ft is the max area
:
If you plot this, y = area and x = width
