document.write( "Question 250431: A landscaper wants to put a cement walk with uniform width around a garden that measures 20x40 feet, She has enough cement to cover 660 ft squared. How wide should it be to us all the cement? \n" ); document.write( "

Algebra.Com's Answer #185096 by Greenfinch(383) $\"\"$ $\"About$

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Assume width to be p feet. Then amount of path is Outside (40 x 20 feet) less the inside (40 - 2p)(20 - 2p) feet
\n" ); document.write( "or 800 - (800 - 80p - 40p +4p^2) = + 120p -4p^2
\n" ); document.write( "This looks right because it is the outside distance (120 feet) times the width of p less the four corners which are p squared in area
\n" ); document.write( "So 120 p - 4 p^2 = 660
\n" ); document.write( "rearranging 4p^2 - 120 p + 660 = 0
\n" ); document.write( "or p^2 - 40 p + 165 = 0
\n" ); document.write( "using formula p = {40 -/+ sqrt{40^2 - (4 x 1 x 165)} }/2
\n" ); document.write( "which I make 20 -/+ sqrt 235
\n" ); document.write( "The - option gives 4.67 feet
\n" ); document.write( "The + option gives 35.33 feet
\n" ); document.write( "The 4.67 is the right option, The other is 40 - 4.67 which is greater than one side of the rectangle. \n" ); document.write( "

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