document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=883351>Question 883351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular field has dimesions 50 m by 40 m. A flowerbed is prepared inside the field with a gravel footpath of equal width around it. The cost of preparing the flowerbed and gravel footpath is Rs.30 and Rs. 20 per sqm respectively amounting to Rs. 52000. Find the width of the footpath.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #533584 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=533584\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular field has dimesions 50 m by 40 m. <BR>\n" );
document.write( "Area of filed = 50*40 2000 m^2\r<BR>\n" );
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document.write( "Let width of footpath be x\r<BR>\n" );
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document.write( "Length of flower bed = (50-2x) <BR>\n" );
document.write( "breadth of flower bed = (40-2x)\r<BR>\n" );
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document.write( "Area of flower bed = (50-2x)(40-2x)<BR>\n" );
document.write( "cost of making flower bed = 30/m^2\r<BR>\n" );
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document.write( "Area of footpath = area of field - area of flower bed\r<BR>\n" );
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document.write( "Area of foot path = (2000-(50-2x)(40-2x))<BR>\n" );
document.write( "cost of making foot path = 20/m^2\r<BR>\n" );
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document.write( "Total cost = 52000\r<BR>\n" );
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document.write( "30(50-2x)(40-2x) +20*(2000-(50-2x)(40-2x))=52000\r<BR>\n" );
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document.write( "30(2000-100x-80x+4x^2)+20(2000-(2000-100x-80x+4x^2))=52000<BR>\n" );
document.write( "60000-5400x+120x^2+ 20(2000-2000+180x-4x^2)=52000\r<BR>\n" );
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document.write( "60000-5400x+120x^2+ 40000-40000+3600x-80x^2)=52000\r<BR>\n" );
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document.write( "60000-1800x+40x^2=52000\r<BR>\n" );
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document.write( "40x^2-1800x+8000=0<BR>\n" );
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document.write( "4x^2-180x+800=0<BR>\n" );
document.write( "4x^2-160x-20x+800=0\r<BR>\n" );
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document.write( "4x(x-40)-20(x-40)=0<BR>\n" );
document.write( "(x-40)(4x-20)=0\r<BR>\n" );
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document.write( "x=40 OR x=5\r<BR>\n" );
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document.write( "it cannot be 40 m since width is 40 m\r<BR>\n" );
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document.write( "so width = 5 m </SPAN>\n" );
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