document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174134>Question 174134</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A brick patio is twice as long as it is wide. It is bordered on all sides by a garden 1.5m wide. Find the dimensions of the patio if the area of the garden is 54m^2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129037 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the width of the patio be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the length of the patio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w ALIGN=MIDDLE  ALT=\"2w\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since the garden is 1.5 meters wide, and the garden goes all the way around, the width of the rectangle formed by the outside edge of the garden must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+%2B+1.5+%2B+1.5=w+%2B+3 ALIGN=MIDDLE  ALT=\"w+%2B+1.5+%2B+1.5=w+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Similarly, the length of the outside rectangle must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w+%2B+3 ALIGN=MIDDLE  ALT=\"2w+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The area of the brick patio is the length times the width or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2 ALIGN=MIDDLE  ALT=\"2w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the area of the entire rectangle including the garden and the patio is again length times width or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282w+%2B+3%29%28w+%2B+3%29+=+2w%5E2+%2B+9w+%2B+9 ALIGN=MIDDLE  ALT=\"%282w+%2B+3%29%28w+%2B+3%29+=+2w%5E2+%2B+9w+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We know the area of the garden part is 54 square meters and the area of the patio part is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2 ALIGN=MIDDLE  ALT=\"2w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the sum of these two quantities must be the overall area.  Now that we have two expressions for the overall area, we can set them equal:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2+%2B+9w+%2B+9+=+2w%5E2+%2B+54 ALIGN=MIDDLE  ALT=\"2w%5E2+%2B+9w+%2B+9+=+2w%5E2+%2B+54\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2w%5E2 ALIGN=MIDDLE  ALT=\"-2w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9w+%2B+9+=+54 ALIGN=MIDDLE  ALT=\"9w+%2B+9+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9w=45 ALIGN=MIDDLE  ALT=\"9w=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9 ALIGN=MIDDLE  ALT=\"1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+5 ALIGN=MIDDLE  ALT=\"w+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > meaning the width of the patio is 5 meters.\r<BR>\n" );
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document.write( "Since the length of the patio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w ALIGN=MIDDLE  ALT=\"2w\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the length must be 10 meters.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Overall area:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2+%2B+9w+%2B+9=2%285%29%5E2%2B9%285%29%2B9=50%2B45%2B9=104 ALIGN=MIDDLE  ALT=\"2w%5E2+%2B+9w+%2B+9=2%285%29%5E2%2B9%285%29%2B9=50%2B45%2B9=104\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area of the patio:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2=2%285%29%5E2=50 ALIGN=MIDDLE  ALT=\"2w%5E2=2%285%29%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Overall area minus the area of the patio must be equal to the area of the garden.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=104-50=54 ALIGN=MIDDLE  ALT=\"104-50=54\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and 54 square meters was the given area of the garden.  Answer checks.\r<BR>\n" );
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