document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285614>Question 285614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle is 4 times as long as it is wide. A second rectangle is 5 centimeters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square centimeters greater than the first. What are the dimensions of the original rectangle?\r<BR>\n" );
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document.write( "I would like to see how to solve the problem in steps, if possible. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207047 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><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=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=207047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=LW ALIGN=MIDDLE  ALT=\"A=LW\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=5L ALIGN=MIDDLE  ALT=\"A=5L\"   DISABLED_style= \"max-width:90%; height:auto;\" > because w=4l. A=LW is the first rectangle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=4L ALIGN=MIDDLE  ALT=\"W=4L\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"A rectangle is 4 times as long as it is wide.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=L%2B5 ALIGN=MIDDLE  ALT=\"X=L%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=W%2B2 ALIGN=MIDDLE  ALT=\"Y=W%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"A second rectangle is 5 centimeters longer and 2 centimeters wider than the first.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XY=A%2B270 ALIGN=MIDDLE  ALT=\"XY=A%2B270\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"The area of the second rectangle is 270 square centimeters greater than the first\" this is the second rectangle.<BR>\n" );
document.write( "so now wee need to substitute to be able to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XY=A%2B270 ALIGN=MIDDLE  ALT=\"XY=A%2B270\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%2B5%29%28W%2B2%29=5L%2B270 ALIGN=MIDDLE  ALT=\"%28L%2B5%29%28W%2B2%29=5L%2B270\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%2B5%29%284L%2B2%29=5L%2B270 ALIGN=MIDDLE  ALT=\"%28L%2B5%29%284L%2B2%29=5L%2B270\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284L%5E2%2B20L%2B2L%2B8%29=5L%2B270 ALIGN=MIDDLE  ALT=\"%284L%5E2%2B20L%2B2L%2B8%29=5L%2B270\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4L%5E2%2B22L-5L%2B8-270=0 ALIGN=MIDDLE  ALT=\"4L%5E2%2B22L-5L%2B8-270=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4L%5E2%2B17L-262=0 ALIGN=MIDDLE  ALT=\"4L%5E2%2B17L-262=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "use the quadratic formula to solve for L, below is the solver to show steps, but for now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=6.24 ALIGN=MIDDLE  ALT=\"L=6.24\"   DISABLED_style= \"max-width:90%; height:auto;\" >or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=-10.49 ALIGN=MIDDLE  ALT=\"L=-10.49\"   DISABLED_style= \"max-width:90%; height:auto;\" > but the lengths cant be negative so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=6.24 ALIGN=MIDDLE  ALT=\"L=6.24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now we can find all the other lengths of the 2 rectangles<BR>\n" );
document.write( "first rectangle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=LW ALIGN=MIDDLE  ALT=\"A=LW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=6.24%2824.96%29 ALIGN=MIDDLE  ALT=\"A=6.24%2824.96%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=155.7504 ALIGN=MIDDLE  ALT=\"A=155.7504\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<p><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=4L ALIGN=MIDDLE  ALT=\"W=4L\"   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%286.24%29 ALIGN=MIDDLE  ALT=\"W=4%286.24%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=24.96 ALIGN=MIDDLE  ALT=\"W=24.96\"   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=X=L%2B5 ALIGN=MIDDLE  ALT=\"X=L%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=%286.24%29%2B5 ALIGN=MIDDLE  ALT=\"X=%286.24%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=11.24 ALIGN=MIDDLE  ALT=\"X=11.24\"   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=Y=W%2B2 ALIGN=MIDDLE  ALT=\"Y=W%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=%2824.96%29%2B2 ALIGN=MIDDLE  ALT=\"Y=%2824.96%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y=26.96 ALIGN=MIDDLE  ALT=\"Y=26.96\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<TABLE  BORDER=1>\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=aL%5E2%2BbL%2Bc=0 ALIGN=MIDDLE  ALT=\"aL%5E2%2BbL%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4L%5E2%2B17L%2B-262+=+0 ALIGN=MIDDLE  ALT=\"4L%5E2%2B17L%2B-262+=+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=L%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"L%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=%2817%29%5E2-4%2A4%2A-262=4481 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2817%29%5E2-4%2A4%2A-262=4481\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4481 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+=+%28-17%2B-sqrt%28+4481+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-17%2B-sqrt%28+4481+%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=L%5B1%5D+=+%28-%2817%29%2Bsqrt%28+4481+%29%29%2F2%5C4+=+6.24253398558978 ALIGN=MIDDLE  ALT=\"L%5B1%5D+=+%28-%2817%29%2Bsqrt%28+4481+%29%29%2F2%5C4+=+6.24253398558978\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B2%5D+=+%28-%2817%29-sqrt%28+4481+%29%29%2F2%5C4+=+-10.4925339855898 ALIGN=MIDDLE  ALT=\"L%5B2%5D+=+%28-%2817%29-sqrt%28+4481+%29%29%2F2%5C4+=+-10.4925339855898\"   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=4L%5E2%2B17L%2B-262 ALIGN=MIDDLE  ALT=\"4L%5E2%2B17L%2B-262\"   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=4L%5E2%2B17L%2B-262+=+4%28L-6.24253398558978%29%2A%28L--10.4925339855898%29 ALIGN=MIDDLE  ALT=\"4L%5E2%2B17L%2B-262+=+4%28L-6.24253398558978%29%2A%28L--10.4925339855898%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6.24253398558978, -10.4925339855898.\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+4%2Ax%5E2%2B17%2Ax%2B-262+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B17%2Ax%2B-262+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );