document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146784>Question 146784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagnol of the rectangle is 15 cm.  Permimeter is 38cm. What is the area?<BR>\n" );
document.write( "Is it possible to find the answer without finding out the dimensions of the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107196 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=107196\">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=P=2%28L%2BW%29 ALIGN=MIDDLE  ALT=\"P=2%28L%2BW%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the perimeter formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38=2%28L%2BW%29 ALIGN=MIDDLE  ALT=\"38=2%28L%2BW%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=38 ALIGN=MIDDLE  ALT=\"P=38\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19=L%2BW ALIGN=MIDDLE  ALT=\"19=L%2BW\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2BW=19 ALIGN=MIDDLE  ALT=\"L%2BW=19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2BW%5E2=D%5E2 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%5E2=D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now move onto the Pythagorean equation dealing with the diagonal and the side lengths\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2BW%5E2=15%5E2 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%5E2=15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=15 ALIGN=MIDDLE  ALT=\"D=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2BW%5E2=225 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%5E2=225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 15 to get 225\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2BW%5E2%2B2LW-2LW=225 ALIGN=MIDDLE  ALT=\"L%5E2%2BW%5E2%2B2LW-2LW=225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add <b>and</b> subtract the quantity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2LW ALIGN=MIDDLE  ALT=\"2LW\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left side. Adding <b>and</b> subtracting the same quantity does not change the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%5E2%2B2LW%2BW%5E2%29-2LW=225 ALIGN=MIDDLE  ALT=\"%28L%5E2%2B2LW%2BW%5E2%29-2LW=225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%2BW%29%5E2-2LW=225 ALIGN=MIDDLE  ALT=\"%28L%2BW%29%5E2-2LW=225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2B2LW%2BW%5E2 ALIGN=MIDDLE  ALT=\"L%5E2%2B2LW%2BW%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%2BW%29%5E2 ALIGN=MIDDLE  ALT=\"%28L%2BW%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2819%29%5E2-2LW=225 ALIGN=MIDDLE  ALT=\"%2819%29%5E2-2LW=225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2BW=19 ALIGN=MIDDLE  ALT=\"L%2BW=19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=361-2LW=225 ALIGN=MIDDLE  ALT=\"361-2LW=225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 19 to get 361\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=361-2A=225 ALIGN=MIDDLE  ALT=\"361-2A=225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LW ALIGN=MIDDLE  ALT=\"LW\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Remember, <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2A=225-361 ALIGN=MIDDLE  ALT=\"-2A=225-361\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=361 ALIGN=MIDDLE  ALT=\"361\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2A=-136 ALIGN=MIDDLE  ALT=\"-2A=-136\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28-136%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"A=%28-136%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=68 ALIGN=MIDDLE  ALT=\"A=68\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=68 ALIGN=MIDDLE  ALT=\"A=68\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So given a diagonal of 15 cm and a perimeter of 38 cm, the area is 68 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: You can go another way and solve for L and W (which turn out to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2819-sqrt%2889%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2819-sqrt%2889%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2819%2Bsqrt%2889%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2819%2Bsqrt%2889%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and find the area by multiplying L and W </SPAN>\n" );
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