document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=892960>Question 892960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help!!!<BR>\n" );
document.write( "Suppose that you need to fence a rectangular play area in your backyard for your child or pet. Further, suppose that you know the length must be 8 feet longer than the width. The back of your house will serve as one side of the fenced area. Note: The perimeter (distance around) of a general rectangle is P = 2L + 2W, and its area is A = L x W. In this situation, P = L + 2W. The value for the area is 4500.\r<BR>\n" );
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document.write( "2.Write the equation of the perimeter in terms of the length, L, only<BR>\n" );
document.write( "P=2W+2L <BR>\n" );
document.write( "Write the area equation in terms of the length, L, only.<BR>\n" );
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document.write( "What can you observe about the characteristics of that quadratic area function? Will this quadratic function’s graph cross the horizontal axis? How do you know?\r<BR>\n" );
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document.write( "Show all your work for finding both the length and the width of this rectangular fenced area.\r<BR>\n" );
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document.write( "Show all your work for calculating the cost of the fence.\r<BR>\n" );
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document.write( "Show all your work for calculating the cost per square foot of the fenced area.)\r<BR>\n" );
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document.write( "What observations and conclusions can you make about the results of them?)<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 #540945 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=540945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> w for width<BR>\n" );
document.write( "L for length<BR>\n" );
document.write( "A for area<BR>\n" );
document.write( "A=4500<BR>\n" );
document.write( "L=8+w<BR>\n" );
document.write( "Using your choice of 1*L to serve as one side of the rectangle region to be fenced, you choose L+2w for the length of fencing to use, c.<BR>\n" );
document.write( "c for length of fencing to use.\r<BR>\n" );
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document.write( "Perimeter of the rectangle region is 2w+2L, but your length of fencing is c=L+2w.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=wL ALIGN=MIDDLE  ALT=\"A=wL\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=w%28w%2B8%29 ALIGN=MIDDLE  ALT=\"A=w%28w%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B8w=A ALIGN=MIDDLE  ALT=\"w%5E2%2B8w=A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B8w-A=0 ALIGN=MIDDLE  ALT=\"w%5E2%2B8w-A=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >------ One unknown variable, w, and one known variable, A as a given constant.<BR>\n" );
document.write( "You have the choice to substitute for A now and if factorable quadratic, then factor the quadratic expression to solve for w; or keep going in symbolic form and substitute for A later.  Seeing so many different factorizations for 4500, my work will be done first in symbolic form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-8%2B-+sqrt%2864-4A%29%29%2F2 ALIGN=MIDDLE  ALT=\"w=%28-8%2B-+sqrt%2864-4A%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-8%2B2sqrt%2816-A%29%29%2F2 ALIGN=MIDDLE  ALT=\"w=%28-8%2B2sqrt%2816-A%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------   The PLUS form will be what is needed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28w=-4%2Bsqrt%2816-A%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28w=-4%2Bsqrt%2816-A%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-4%2Bsqrt%2816%2B4500%29 ALIGN=MIDDLE  ALT=\"w=-4%2Bsqrt%2816%2B4500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=-4%2Bsqrt%284516%29%29 ALIGN=MIDDLE  ALT=\"highlight%28w=-4%2Bsqrt%284516%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, keeping like this for now.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=wL=4500 ALIGN=MIDDLE  ALT=\"wL=4500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=4500%2Fw ALIGN=MIDDLE  ALT=\"L=4500%2Fw\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=4500%2F%28-4%2Bsqrt%284516%29%29 ALIGN=MIDDLE  ALT=\"L=4500%2F%28-4%2Bsqrt%284516%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you rationalize the denominator and simplify (not showing those steps here),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L=%284500%2B1125sqrt%284516%29%29%2F1133%29 ALIGN=MIDDLE  ALT=\"highlight%28L=%284500%2B1125sqrt%284516%29%29%2F1133%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----not simplifiable further.\r<BR>\n" );
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document.write( "The amount of fence material c=L+2w<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=%284500%2B1125sqrt%284516%29%29%2F1133%29%2B2sqrt%284516%29-8%29 ALIGN=MIDDLE  ALT=\"highlight%28c=%284500%2B1125sqrt%284516%29%29%2F1133%29%2B2sqrt%284516%29-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can then compute this as a decimal approximation if needed.<BR>\n" );
document.write( "You could also first compute L and w and then find the value for c. </SPAN>\n" );
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