SOLUTION: The sum of the length l and width w of a rectangular region is 190 meters. Find the dimensions that produce the greatest (optimal) area.

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Question 851257: The sum of the length l and width w of a rectangular region is 190 meters. Find the dimensions that produce the greatest (optimal) area.
Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
What are the possible lengths and widths (assuming whole numbers)? The greatest area is going to be those numbers that are closest in value. Think about it. A long, skinny rectangle of 189 by 1 will be 189*1=189 m^2 while 180*10 will be 1800 m^2. So it's only logical that the greatest would be the numbers closest to each other.
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For 190, that would be 95 and 95.
95*95 = 9025 m^2
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Test it out. Try 90 * 100. 9000 m^2. Close, but not higher. What about 94*96? 9024m^2. Almost!
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This is less a math problem than a logic problem :-)