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Suppose that a strip of uniform width is plowed along both sides and both ends of a garden that is 120 ft long by 90 ft wide.
\n" ); document.write( " How wide is the strip, if the garden is one-half plowed?
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\n" ); document.write( "Find the total area of the garden: 120 * 90 = 10800 sq/ft
\n" ); document.write( "Find half the area of the garden: 10800/2 = 5400 sq/ft
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\n" ); document.write( "Let x = the width of the plowed strip all the way around.
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\n" ); document.write( "The dimension of the unplowed area will be (120-2x) by (90-2x)
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\n" ); document.write( "We know the area of the unplowed = the area of the plowed (5400 sq/ft)
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\n" ); document.write( "Plowed area = unplowed area
\n" ); document.write( "(120-2x)*(90-2x) = 5400
\n" ); document.write( "FOIL
\n" ); document.write( "10800 - 240x - 180x + 4x^2 = 5400
\n" ); document.write( "Combine like terms
\n" ); document.write( "4x^2 - 420x + 10800 - 5400 = 0
\n" ); document.write( "4x^2 - 420x + 5400 = 0
\n" ); document.write( "Simplify divide by 4
\n" ); document.write( "x^2 - 105x + 1350 = 0
\n" ); document.write( "You can use the quadratic formula to solve this, but it will factor to:
\n" ); document.write( "(x-90)(x-15) = 0
\n" ); document.write( "only one solution will make sense here
\n" ); document.write( "x = 15 ft is the width of the plowed strip
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\n" ); document.write( "See if this checks out
\n" ); document.write( "(120-2(15)) * (90-2(15) =
\n" ); document.write( "90 * 60 = 5400 sq/ft which is half the total area \n" ); document.write( "