document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854488>Question 854488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a park is installing a rectangular reflecting pool surrounded by a concrete walkway of uniform width. the reflecting pool will measure 42 ft by 26 ft. there is enough concrete to cover 460 ft^3 for the walkway. what is the maximum width of the walkway?<BR>\n" );
document.write( "how can drawing a diagram help you solve this problem <BR>\n" );
document.write( "how can you write an expression in terms of x for the area of the walkway </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514787 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> NOTE:<BR>\n" );
document.write( "The problem should state that \" there is enough concrete to cover 460 ft^2 for the walkway,\" because measure of the surface to be covered has to be in square feet. Cubic feet is a measure of volume, and if you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=460+ft%5E3 ALIGN=MIDDLE  ALT=\"460+ft%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > you should ask how deep they want the walkway. Do they want the concrete slabs to be 2 inches thick? Thicker than that? <BR>\n" );
document.write( " <BR>\n" );
document.write( "Drawing not to scale:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-30%2C30%2C-20%2C20%2C%0D%0Ablue%28rectangle%28-20%2C-11%2C20%2C11%29%29%2C%0D%0Ared%28rectangle%28-27%2C-18%2C27%2C18%29%29%2C%0D%0Aarrow%28-27%2C0%2C-20%2C0%29%2Carrow%28-20%2C0%2C-27%2C0%29%2C%0D%0Aarrow%280%2C-18%2C0%2C-11%29%2Carrow%280%2C-11%2C0%2C-18%29%2C%0D%0Alocate%28-24%2C0%2Cx%29%2Clocate%280.3%2C-13%2Cx%29%2C%0D%0Alocate%28-2%2C5%2C42ft%29%2Clocate%2810%2C1%2C26ft%29%2C%0D%0Aarrow%2812%2C2%2C12%2C11%29%2Carrow%2812%2C-2%2C12%2C-11%29%2C%0D%0Aarrow%28-5%2C4%2C-20%2C4%29%2Carrow%285%2C4%2C20%2C4%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "How can drawing a diagram help you solve this problem?<BR>\n" );
document.write( "A drawing will help you realize that<BR>\n" );
document.write( "the reflecting pool is a rectangle (blue in my drawing);<BR>\n" );
document.write( "there is a bigger rectangle formed by the walkway plus the reflecting pool (red in my drawing), and<BR>\n" );
document.write( "the surface area of the walkway is the difference of the areas of the two rectangles.<BR>\n" );
document.write( "You would also notice that if<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= uniform width of the walkway (in ft),<BR>\n" );
document.write( "the length and width (in ft) of the larger rectangle will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B42%29 ALIGN=MIDDLE  ALT=\"%282x%2B42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B36%29 ALIGN=MIDDLE  ALT=\"%282x%2B36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "How can you write an expression in terms of x for the area of the walkway?<BR>\n" );
document.write( "You can express the area (in square feet) of the smaller rectangle as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2A26 ALIGN=MIDDLE  ALT=\"42%2A26\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You can express the area (in square feet) of the bigger rectangle as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2842%2B2x%29%2A%2826%2B2x%29 ALIGN=MIDDLE  ALT=\"%2842%2B2x%29%2A%2826%2B2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=4x^2+84x+52x+42*26=4x^2+136x+42*26}}} .<BR>\n" );
document.write( "You can express the area (in square feet) of the walkway as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B136x%2B42%2A26-42%2A26=highlight%284x%5E2%2B136x%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B136x%2B42%2A26-42%2A26=highlight%284x%5E2%2B136x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "What is the maximum width of the walkway?<BR>\n" );
document.write( "You need to make that area equal or smaller than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=460ft%5E2 ALIGN=MIDDLE  ALT=\"460ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (460 square feet).<BR>\n" );
document.write( "So the maximum will happen when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B136x=460 ALIGN=MIDDLE  ALT=\"4x%5E2%2B136x=460\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B136x-460=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B136x-460=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides of the equal sign (everything) by 4, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B34x-115=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B34x-115=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Applying the quadratic formula we find<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-34+%2B-+sqrt%2834%5E2-4%2A1%2A%28-115%29%29%29%2F%282%2A1%29=%28-34+%2B-+sqrt%281156%2B460%0D%0A%29%29%2F2=%28-34+%2B-+sqrt%281616%29%29%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >= about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-34+%2B-+40.2000%29%2F2 ALIGN=MIDDLE  ALT=\"%28-34+%2B-+40.2000%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We discard the negative solution, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-34+-+40.2000%29%2F2 ALIGN=MIDDLE  ALT=\"%28-34+-+40.2000%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and are left with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-34+%2B+40.2000%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-34+%2B+40.2000%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=about3.1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=about3.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the maximum width of the walkway is 3.1 feet. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );