document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187640>Question 1187640</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular playground has a walkway around it with a width of x-2.  The garden is 36 m by 20 m.  <BR>\n" );
document.write( "Find an expression for the combined area of the playground and the walkway around it<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818651 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the length becomes 36 + 2 * (x - 2) which becomes 36 + 2x - 4 which becomes 32 + 2x.<BR>\n" );
document.write( "the width becomes 20 + 2 * (x-2) which becomes 20 + 2x - 4 which becomes 16 + 2x.\r<BR>\n" );
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document.write( "the new dimensions are (32 + 2x) for the length and 16 + 2x for the width.\r<BR>\n" );
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document.write( "the combined area is (32 + 2x) * (16 + 2x) = 4x^2 + 96x + 512.\r<BR>\n" );
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document.write( "your equation for the combined area will be 4x^2 + 96x + 512 or (32 + 2x) * (16 + 2x).\r<BR>\n" );
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document.write( "note that x must be greater than 2, otherwise the combined area will be less than the original area.\r<BR>\n" );
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document.write( "the original area is 36 * 20 = 720<BR>\n" );
document.write( "when x = 2, the combined area will be (32 + 4) * (16 + 4) = 36 * 20 = 720.<BR>\n" );
document.write( "that's breakeven point.<BR>\n" );
document.write( "for the path to have any width, x has to be greater than 2.<BR>\n" );
document.write( "as a practical matter, if you want the path to be at least 2 feet wide, then x should be greater than or equal to 3.\r<BR>\n" );
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document.write( "the following graph shows the relationship.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/111203.jpg\" >\r<BR>\n" );
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document.write( "as you can see, when x = 3, the combined area is 836 square feet.\r<BR>\n" );
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document.write( "that's because 32 + 2 * 3 = 38 and 16 + 2 * 3 = 22 and 38 * 22 = 836 square feet.\r<BR>\n" );
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document.write( "here's a diagram of what this would look like:\r<BR>\n" );
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document.write( "when x = 3, the value of A in the diagram is x - 2 which becomes 3 - 2 which becomes 1.<BR>\n" );
document.write( "when x = 3, the value of A is 1.<BR>\n" );
document.write( "the length is 36 + 2A = 38.<BR>\n" );
document.write( "the width is 20 + 2A = 22.<BR>\n" );
document.write( "the area is 38 * 22 = 836.\r<BR>\n" );
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document.write( "that's the same value on the graph when x = 3.\r<BR>\n" );
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