SOLUTION: James has 66 yards of fencing. Each fence panel is 3/4 yard long. James wants to fence a rectangular section of his yard. What is the largest possible rectangular area he could fen

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Question 1005005: James has 66 yards of fencing. Each fence panel is 3/4 yard long. James wants to fence a rectangular section of his yard. What is the largest possible rectangular area he could fence in? How many fence panels will there be on each side of the rectangular area?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+66%2F%283%2F4%29+=+88+ is the number of panels
Let +A+ = area of rectangle
Let +w+ = the width of rectangle
The length = +%28+88+-+2w+%29%2F2+=+44+-+w+
+A+=+w%2A%28+44+-+w+%29+
+A+=+44w+-+w%5E2+
If I find the roots:
+-w%5E2+%2B+44w+=+0+
+w%2A%28+-w+%2B+44+%29+=+0+
+w+=+0+ and
+w+=+44+
are the roots
The peak of the parabola is midway between at +w+=+22+
The length = +44+-+w+=+44+-+22+
+44+-+22+=+22+
The rectangle that maximizes area is a 22 x 22 square of panels
Here's the plot of area and number of panels
The peak is at +A+=+22%2A22+ which is +A+=+484+
( measured in square panels where 1 panel is the unit of measure )
+graph%28+400%2C+400%2C+-5%2C+50%2C+-50%2C600%2C+-x%5E2+%2B+44x+%29+