document.write( "Question 35991: Please help\r
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document.write( "4)Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.\r
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document.write( "Answer:
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Algebra.Com's Answer #22403 by venugopalramana(3286)![]() ![]() You can put this solution on YOUR website! SEE THE FOLLOWING AND TRY \n" ); document.write( "LET LENGTH BE L AND WIDTH BE W \n" ); document.write( "WE HAVE PERIMETER =2(L+W)=300 \n" ); document.write( "L+W=150 \n" ); document.write( "W=150-L.............................I \n" ); document.write( "AREA =LW=L(150-L)= - (L^2-150L) = - {(L^2-2*L*75+75^2)-75^2} \n" ); document.write( "= 75^2 - (L-75)^2.......SINCE (L-75)^2 IS ALWAYS POSITIVE ,AND IT IS \n" ); document.write( "TO BE SUBTRACTED FROM 75^2 TO GET THE AREA,WE GET MAXIMUM AREA WHEN \n" ); document.write( "THIS IS MINIMUM...OR...L-75=0....OR....L=75 \n" ); document.write( "SO FOR MAXIMUM AREA THE PATIO SHOULD BE A SQUARE OF 75' LENGTH AND 75' WIDTH. \n" ); document.write( " |