document.write( "Question 1166231: A man mows his 40 foot by 50 foot rectangular lawn in a spiral pattern starting from the outside edge. After a bit of hard work he stops for a water break he is 90% done. How wide of a strip has he mowed around the outside edge? \n" ); document.write( "

Algebra.Com's Answer #790742 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A man mows his 40 foot by 50 foot rectangular lawn in a spiral pattern starting from the outside edge.
\n" ); document.write( " After a bit of hard work he stops for a water break he is 90% done.
\n" ); document.write( " How wide of a strip has he mowed around the outside edge?
\n" ); document.write( ":
\n" ); document.write( "find the total area of the lawn: 40 * 50 = 2000 sq/ft
\n" ); document.write( "Find the area of the 10% that remains to be mowed, after 90% is mowed\
\n" ); document.write( ".10 * 2000 = 200 sq/ft
\n" ); document.write( ":
\n" ); document.write( "let x = the width of the mowed strip
\n" ); document.write( "(40-2x)(50-2x) = 200
\n" ); document.write( "FOIL
\n" ); document.write( "2000 - 80x - 100x + 4x^2 = 200
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "4x^2 - 180x + 2000 - 200 = 0
\n" ); document.write( "4x^2 - 180x + 1800 = 0
\n" ); document.write( "simplify, divide by 4
\n" ); document.write( "x^2 - 45x + 450 = 0
\n" ); document.write( "(x-15)(x-30) = 0
\n" ); document.write( "Two solutions
\n" ); document.write( "x = 15 and x = 30 but only x=15 is reasonable (if x=30, 2x would = 60)
\n" ); document.write( "The width of the mowed strip = 15 ft
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this; find the area of the unmowed lawn
\n" ); document.write( "(40-30)*(50-30) = 200
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