SOLUTION: Find the maximum area of a rectangle with a perimeter of 56.

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Question 739757: Find the maximum area of a rectangle with a perimeter of 56.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +L+ = the length
Let +W+ = the width
Let +P+ = the perimeter
Let +A+ = the area
--------------------
+P+=+56+
+P+=+2W+%2B+2L+
+56+=+2W+%2B+2L+
+W+%2B+L+=+28+
+L+=+28+-+W+
---------------
+A+=+W%2AL+
+A+=+W%2A%28+28+-+W+%29+
+A+=+-W%5E2+%2B+28W+
-------------------
This is a parabola with a maximum due
to the minus sign in front of the +W%5E2+
The W-coordinate of the maximum is at
+W%5Bmax%5D+=+-b%2F%282a%29+ where
+a+=+-1+
+b+=+28+
+W%5Bmax%5D+=+-28+%2F+%282%2A%28-1%29%29+
+W%5Bmax%5D+=+14+
and
+A%5Bmax%5D+=+W%2A%28+28+-+W+%29+
+A%5Bmax%5D+=+14%2A14+
+A%5Bmax%5D+=+196+
-----------------
Here's a plot of this equation:
+graph%28+400%2C+400%2C+-5%2C+40%2C+-10%2C+220+%2C+-x%5E2+%2B+28x+%29+