document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207877>Question 207877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular pool is 14 metres long and 6 metres wide. It is surrounded by a pebble path of uniform width <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > metres. If the area of the path is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96m%5E2 ALIGN=MIDDLE  ALT=\"96m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the width.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157239 by </B><A HREF=/tutors/aboutme.mpl?userid=pjalgeb><B>pjalgeb(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pjalgeb><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:\r<BR>\n" );
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document.write( "Length of Pool = 14 metres<BR>\n" );
document.write( "Width of Pool = 6 metres<BR>\n" );
document.write( "Area of Path = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96m%5E2 ALIGN=MIDDLE  ALT=\"96m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Required:\r<BR>\n" );
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document.write( " x = Width of Path = ?\r<BR>\n" );
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document.write( "Solution:\r<BR>\n" );
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document.write( "Area of Pool = L x W <BR>\n" );
document.write( "             = 14m x 6m<BR>\n" );
document.write( "             = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84+m%5E2 ALIGN=MIDDLE  ALT=\"84+m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area of Path = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96m%5E2 ALIGN=MIDDLE  ALT=\"96m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Total Area = Area of Pool + Area of Path<BR>\n" );
document.write( "           = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84m%5E2 ALIGN=MIDDLE  ALT=\"84m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96m%5E2 ALIGN=MIDDLE  ALT=\"96m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "           = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=160m%5E2 ALIGN=MIDDLE  ALT=\"160m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because the pebble path is of uniform width, then the equation for total area is:\r<BR>\n" );
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document.write( "(Length of Pool+Width of Path)* (Width of Pool +Width of Path) = Total Area\r<BR>\n" );
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document.write( "or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B14%29%2A%282x+%2B+6%29+=+160 ALIGN=MIDDLE  ALT=\"%282x+%2B14%29%2A%282x+%2B+6%29+=+160\"   DISABLED_style= \"max-width:90%; height:auto;\" >      --> We use 2x because the path is on both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+%2B+28x+%2B+12x+%2B+84+=+160 ALIGN=MIDDLE  ALT=\"4x%5E2+%2B+28x+%2B+12x+%2B+84+=+160\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> Distributive Property\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+%2B+40x+%2B+84+=+160 ALIGN=MIDDLE  ALT=\"4x%5E2+%2B+40x+%2B+84+=+160\"   DISABLED_style= \"max-width:90%; height:auto;\" >        --> Combine Like Terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2+%2B+40x+%2B+84%29%2F4+=+160%2F4 ALIGN=MIDDLE  ALT=\"%284x%5E2+%2B+40x+%2B+84%29%2F4+=+160%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> Divide both sides by 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10x+%2B+21+=+40 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10x+%2B+21+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" >         --> The result is a quadratic equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10x+%2B+21+-+21+=+40-21 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10x+%2B+21+-+21+=+40-21\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> Subtract 21 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10x+=+19 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10x+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" >              --> The resulting equation can be solved by method of completing the square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10x+%2B+25=+19+%2B+25+ ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10x+%2B+25=+19+%2B+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" >     -->Add 25 to both sides to complete the square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10x+%2B+25=+44+ ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10x+%2B+25=+44+\"   DISABLED_style= \"max-width:90%; height:auto;\" >          -->The left side is now a perfect square trinomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+5%29%5E2=+44+ ALIGN=MIDDLE  ALT=\"%28x+%2B+5%29%5E2=+44+\"   DISABLED_style= \"max-width:90%; height:auto;\" >                -->Factor the left side to a perfect binomial square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x+%2B+5%29%5E2%29=+sqrt%2844%29+ ALIGN=MIDDLE  ALT=\"sqrt%28%28x+%2B+5%29%5E2%29=+sqrt%2844%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    -->We can now solve for X by finding the square root of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B5+=+%2B-+sqrt%2844%29+ ALIGN=MIDDLE  ALT=\"+x%2B5+=+%2B-+sqrt%2844%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >         --> Even radicals have two roots(+ and -)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B5+=+%2B-+sqrt%284%2A11%29%29+ ALIGN=MIDDLE  ALT=\"+x%2B5+=+%2B-+sqrt%284%2A11%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    -->Factor the Radicand into 4 and 11\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B5+=+%2B-+2sqrt%2811%29%29+ ALIGN=MIDDLE  ALT=\"+x%2B5+=+%2B-+2sqrt%2811%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    --> The square root of 4 is 2, so this can be moved out of the radical\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=+-5+%2B-+2sqrt%2811%29%29+ ALIGN=MIDDLE  ALT=\"+x=+-5+%2B-+2sqrt%2811%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    --> There is no such thing as negative length so we use the other answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=+-5+%2B+2sqrt%2811%29%29+ ALIGN=MIDDLE  ALT=\"+x=+-5+%2B+2sqrt%2811%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    --> This is the simplified answer \r<BR>\n" );
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document.write( "or by using calculator we get:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.633 ALIGN=MIDDLE  ALT=\"x+=+1.633\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Lets check our answer:\r<BR>\n" );
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document.write( "               (2x+14)(2x+6) = 160   --> From the equation for the total area<BR>\n" );
document.write( "[2(1.633) + 14][2(1.633) +6] = 160   --> Substitute the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with our answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.633 ALIGN=MIDDLE  ALT=\"1.633\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "             (17.266)(9.266) = 160<BR>\n" );
document.write( "                         160 = 160                            \r<BR>\n" );
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document.write( "Answer: \r<BR>\n" );
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document.write( "The width of the path is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.633 ALIGN=MIDDLE  ALT=\"1.633\"   DISABLED_style= \"max-width:90%; height:auto;\" > metres.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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