SOLUTION: An architect is designing an atrium for a hotel. The atrium is to be rectangular with a perimeter of 700 ft of brass piping. What dimensions will maximize the area of the​ at

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Question 1114191: An architect is designing an atrium for a hotel. The atrium is to be rectangular with a perimeter of 700 ft of brass piping. What dimensions will maximize the area of the​ atrium?
A rectangle has a horizontal side labeled W and a vertical side labeled L.
The largest rectangular area of the atrium is
______ by______.
There might be more after this, but at the moment, this is all of the problem I have. Thank you in advance for your time.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I should end up with a square to maximize area.
The perimeter is +P+=+700+ ft
+P+=+2W+%2B+2L+
+2W+%2B+2L+=+700+
+2L+=+700+-+2W+
+L+=+350+-+W+ ft
-----------------------
The area, +A+=+W%2AL+
+A+=+W%2A%28+350+-+W+%29+
+A+=+-W%5E2+%2B+350W+ ft2
------------------------
The formula for the W-value of the vetex,
( maximum in his case ) is
+W%5Bmax%5D+=+-b%2F%282a%29+ when the general form is:
+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+W%5Bmax%5D+=+-350%2F%28-2%29+
+W%5Bmax%5D+=+175+
and
+L%5Bmax%5D+=+350+-+175+
+L%5Bmax%5D+=+175+
---------------------------
+A%5Bmax%5D+=+W%5Bmax%5D%2AL%5Bmax%5D+
+A%5Bmax%5D+=+175%2A175+
So the max area is a square. You can calculate
and check my math.
Note also:
+P+=+2W+%2B+2L+
+P+=+2%2A175+%2B+2%2A175+
+P+=+700+
as it should