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A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of
\n" ); document.write( " uniform width is to be built around the garden.
\n" ); document.write( "How wide can the path be, if there is enough gravel for 516 square feet?
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\n" ); document.write( "Let x = the width of the path required to utilize 516 sq/ft of gravel
\n" ); document.write( "then
\n" ); document.write( "The overall dimensions (including the path) are: (2x+18) by (2x+13)
\n" ); document.write( "FOIL this and we have:
\n" ); document.write( "4x^2 + 62x + 234 = the area of the garden and the path
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\n" ); document.write( "18 * 13 = 234, the area of the garden
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\n" ); document.write( "Overall area - garden area = path area (516 sq/ft)
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\n" ); document.write( "(4x^2 + 62x + 234) - 234 = 516
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\n" ); document.write( "4x^2 + 62x - 516 = 0
\n" ); document.write( "Simplify divide by 2:
\n" ); document.write( "2x^2 + 31x - 258 = 0
\n" ); document.write( "This will factor:
\n" ); document.write( "(2x + 43)(x - 6) = 0
\n" ); document.write( "Positive solution
\n" ); document.write( "x = + 6 ft is the width of the path
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\n" ); document.write( "Check our solution:
\n" ); document.write( "overall dimensions would be 30 by 25 = 750 sq/ft (add 12 to length & width)
\n" ); document.write( "750 - 234 = 516, the area of the path
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\n" ); document.write( "Did this clear up some of the difficulty you were having here? \n" ); document.write( "