document.write( "Question 59540: a garden area is 30ft long and 20ft wide. a path of uniform width is set around the edge. if the remaining garden is 400ft squared.what is the width of the path? \n" ); document.write( "
Algebra.Com's Answer #40852 by stanbon(75887)\"\" \"About 
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Draw the picture with one rectangle inside another.
\n" ); document.write( "The inner rectangle area is 400 sq ft.
\n" ); document.write( "The outer rectangle has area 600 sq ft including the path area.
\n" ); document.write( "Let the path have uniform width of \"x\" ft.
\n" ); document.write( "Notice the four rectangles nor surrounding the inner
\n" ); document.write( "rectangle.
\n" ); document.write( "Two of them are 20 ft by x ft: Area of each is 20x ft: Total for the two is 40x
\n" ); document.write( "Two of them are (30-2x) by x ft: Area of each of these is 30x-2x^2; Total for
\n" ); document.write( "the two is 60x-4x^2'
\n" ); document.write( "EQUATION:
\n" ); document.write( "Outer rectangle area - inner rectangle area =200 sq ft.
\n" ); document.write( "The path covers that 200 sq ft.
\n" ); document.write( "Path area = 40x+60x-4x^2 = 200 sq ft.
\n" ); document.write( "4x^2-100x+200=0
\n" ); document.write( "x^2-25x+50=0
\n" ); document.write( "x=[25+-sqrt(25^2-4*50]/2
\n" ); document.write( "x=[25+-sqrt(425)]/2
\n" ); document.write( "x=[25+-5sqrt17]/2
\n" ); document.write( "x=4.38/2=2.1922 ft. (width of the sidewalk)
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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