document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214239>Question 214239</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0495117935/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The frame around the picture in the illustration has a constant width. how wide is the frame if the area equals the area of the picture\r<BR>\n" );
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document.write( "                      the illustration is a square inside a squre. the frame<BR>\n" );
document.write( "                      with a width of 12 inches and a hight of 10 inches \r<BR>\n" );
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document.write( "I hope thats enough info 2 help me <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 #162090 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=162090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The frame around the picture in the illustration has a constant width. how wide is the frame if the area equals the area of the picture<BR>\n" );
document.write( "the illustration is a square inside a squre. the frame<BR>\n" );
document.write( "with a width of 12 inches and a hight of 10 inches<BR>\n" );
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document.write( "Draw a diagram of the problem, label all the information given it'll help you see the solution.<BR>\n" );
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document.write( "Let w = width of frame<BR>\n" );
document.write( "then measure of picture is:<BR>\n" );
document.write( "12-2w = width of picture<BR>\n" );
document.write( "10-2w = length of picture<BR>\n" );
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document.write( "Area of picture is (length times width):<BR>\n" );
document.write( "(12-2w)(10-2w)<BR>\n" );
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document.write( "Area of frame:<BR>\n" );
document.write( "2(10w) + 2w(12-2w)<BR>\n" );
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document.write( "Setting them equal\":<BR>\n" );
document.write( "(12-2w)(10-2w) = 2(10w) + 2w(12-2w)<BR>\n" );
document.write( "120-24w-20w+4w^2 = 20w + 24w - 4w^2<BR>\n" );
document.write( "120-44w+4w^2 = 44w - 4w^2<BR>\n" );
document.write( "8w^2+120-44w = 44w<BR>\n" );
document.write( "8w^2-88w+120 = 0<BR>\n" );
document.write( "w^2-11w+15 = 0<BR>\n" );
document.write( "Using the quadratic equation we get two solutions:<BR>\n" );
document.write( "w={9.40512483795333, 1.59487516204667}<BR>\n" );
document.write( "It wouldn't make sense to have a 9+ inch width frame so the answer MUST be:<BR>\n" );
document.write( "w = 1.595 inches (width of frame)<BR>\n" );
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document.write( "Details of the quadratic equation to follow:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aw%5E2%2Bbw%2Bc=0 ALIGN=MIDDLE  ALT=\"aw%5E2%2Bbw%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1w%5E2%2B-11w%2B15+=+0 ALIGN=MIDDLE  ALT=\"1w%5E2%2B-11w%2B15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-11%29%5E2-4%2A1%2A15=61 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-11%29%5E2-4%2A1%2A15=61\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=61 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--11%2B-sqrt%28+61+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--11%2B-sqrt%28+61+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+61+%29%29%2F2%5C1+=+9.40512483795333 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+61+%29%29%2F2%5C1+=+9.40512483795333\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B2%5D+=+%28-%28-11%29-sqrt%28+61+%29%29%2F2%5C1+=+1.59487516204667 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%28-11%29-sqrt%28+61+%29%29%2F2%5C1+=+1.59487516204667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1w%5E2%2B-11w%2B15 ALIGN=MIDDLE  ALT=\"1w%5E2%2B-11w%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1w%5E2%2B-11w%2B15+=+1%28w-9.40512483795333%29%2A%28w-1.59487516204667%29 ALIGN=MIDDLE  ALT=\"1w%5E2%2B-11w%2B15+=+1%28w-9.40512483795333%29%2A%28w-1.59487516204667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 9.40512483795333, 1.59487516204667.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-11%2Ax%2B15+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-11%2Ax%2B15+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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