document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=801765>Question 801765</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonals of a rhombus differ by 4. If its perimeter is 40, find its area. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #483626 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=483626\">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=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >= length of one side of the rhombus (because the perimeter, 40, is the sum of 4 such side lengths)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= length of the shortest diagonal <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B4=2%28x%2B2%29 ALIGN=MIDDLE  ALT=\"2x%2B4=2%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= length of the longer diagonal (because it is 4 more than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-9%2C9%2C-9%2C9%2C%0D%0Aline%28-6%2C0%2C0%2C8%29%2Cline%280%2C-8%2C6%2C0%29%2C%0D%0Atriangle%28-6%2C0%2C0%2C0%2C0%2C-8%29%2C%0D%0Agreen%28triangle%286%2C0%2C0%2C0%2C0%2C8%29%29%2C%0D%0Agreen%28rectangle%280%2C0%2C0.5%2C0.5%29%29%2C%0D%0Alocate%282.5%2C0%2Cx%29%2Clocate%280.2%2C3.8%2Cx%2B2%29%2C%0D%0Alocate%283%2C5%2C10%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The diagonals dplit the rhombus into 4 congruent triangles.<BR>\n" );
document.write( "Applying the Pythagorean theorem to one of those 4 triangles, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B2%29%5E2=10%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B2%29%5E2=10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2%2B4x%2B4=100 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B4x%2B4=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x%2B4=100 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x%2B4=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x-96=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x-96=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides of the equal sign by 2, the equation simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-48=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving by factoring is easy.<BR>\n" );
document.write( "Factoring we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B8%29%28x-6%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B8%29%28x-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > with solutions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since a negative length does not make sense the solution is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=8 ALIGN=MIDDLE  ALT=\"x%2B2=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of the rhombus is the area of the 4 triangles<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A6%2A8=highlight%2896%29 ALIGN=MIDDLE  ALT=\"2%2A6%2A8=highlight%2896%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );