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Question 1072459: The owner of the Rancho Grande has 2952 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area he can enclose?
shorter side = ?yd
Longer side = ?yd
what is the area = ?yd^2
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It helps to draw this.
two sides are each x
the one length is 2952-2x
the area is x(2952-2x)=-2x^2+2952x.
The derivative of that is -4x+2952.
Set it equal to 0 and -4x=-2952 and x=738 yds
2x=1476 yds
A=1,089,288 yd^2
That is the typical answer in these questions, where the width is half the length.
Can check with a very close width and length, like 736 and 1480, the product of which is 1,089,280 yd^2.
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