document.write( "Question 1060742: A rectangle has a perimeter of 20 meters.3 rectangles were made 1x20, 2x10, and 4x5. How do I find the dimensions of the rectangle with the greatest area. And how do I find the dimensions of the rectangle with the least area \n" ); document.write( "
Algebra.Com's Answer #675619 by Boreal(15235)\"\" \"About 
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perimeter is 20, so make length x
\n" ); document.write( "width is 10-x, since length + width = half the perimeter
\n" ); document.write( "area is x(10-x)=10x-x^2
\n" ); document.write( "The derivative of that is 10-2x=0
\n" ); document.write( "2x=10
\n" ); document.write( "x=5 meters, which is a square 5 meters on a side.
\n" ); document.write( "The second derivative is -2. This is differentiable throughout, and the negative second derivative makes it a maximum.
\n" ); document.write( "The maximum area of a rectangle with fixed perimeter occurs when the rectangle is a square.
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\n" ); document.write( "As the rectangle becomes longer and narrower, the area becomes less
\n" ); document.write( "at 1*9 (perimeter 20) the area is 9
\n" ); document.write( "at 0.5*9.5 (perimeter also 20), the area is 4.75
\n" ); document.write( "at 0.1*9.9, the area is 0.99
\n" ); document.write( "at 0.01*9.99, the area is 0.0999.
\n" ); document.write( "the dimensions of the rectangle with the least area approach 10 by 0. \r
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