document.write( "Question 628653: Find the length and width of a rectangle that has area 55 square centimeters and a minimum perimeter. Round your answer to one decimal place. \n" ); document.write( "

Algebra.Com's Answer #395775 by josmiceli(19441) $\"\"$ $\"About$

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$\"+A+=+L%2AW+\"$
\n" ); document.write( " $\"+55+=+L%2AW+\"$
\n" ); document.write( " $\"+W+=+55%2FL+\"$
\n" ); document.write( "------------
\n" ); document.write( "The formula for perimeter is
\n" ); document.write( " $\"+P+=+2W+%2B+2L+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+P+=+2%2A%28+55%2FL+%29+%2B+2L+\"$
\n" ); document.write( " $\"+P+=+110%2FL+%2B+2L+\"$
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-2%2C+16%2C+-5%2C+50%2C+110%2Fx+%2B+2x+%29+\"$
\n" ); document.write( "The minimum perimeter is around $\"+P+=+30+\"$
\n" ); document.write( "and $\"+L+=+7.5+\"$
\n" ); document.write( "Since $\"++sqrt%2855%29+=+7.416+\"$ ., and $\"+4%2A7.416+=+29.665+\"$ ,
\n" ); document.write( "It looks like the perimeter is minimum when the
\n" ); document.write( "rectangle is a square.
\n" ); document.write( " $\"+P%5Bmin%5D+=+29.7+\"$
\n" ); document.write( "OK \n" ); document.write( "

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