document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=523748>Question 523748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One diagonal of a rhombus has the same length, 10cm, as each side. How long is the other diagonal </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #347414 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=347414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One diagonal of a rhombus has the same length, 10cm, as each side. How long is the other diagonal\r<BR>\n" );
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document.write( "Then it it is two equilateral triangles with a common side, like this,<BR>\n" );
document.write( "where all the black line segments are 10 cm each:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%283000%2F11%2C400%2C-.5%2C2.5%2C-2.2%2C2.2%2C+triangle%280%2C0%2C2%2C0%2C1%2Csqrt%283%29%29%2C%0D%0Atriangle%280%2C0%2C2%2C0%2C1%2C-sqrt%283%29%29%2C+locate%28.1%2C.9%2C10cm%29%2C%0D%0A%0D%0A%0D%0Agreen%28line%281%2Csqrt%283%29%2C1%2C-sqrt%283%29%29%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We want to know the length of the green line segment:\r<BR>\n" );
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document.write( "So we look at just one half of the top which is this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%283000%2F11%2C400%2C-.5%2C2.5%2C-2.2%2C2.2%2C+triangle%280%2C0%2C1%2C0%2C1%2Csqrt%283%29%29%2C%0D%0Alocate%28.1%2C.9%2C10cm%29%2C+locate%28.5%2C0%2C5cm%29%2C+%0D%0Agreen%28line%281%2Csqrt%283%29%2C1%2C0%29%2Clocate%281.1%2C.8%2Cb%29%29%0D%0A++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The bottom side is 5cm because the diagonals of a parallelogram bisect<BR>\n" );
document.write( "each other (and a rhombus is a parallelogram). The hypotenuse is a side<BR>\n" );
document.write( "of the rhombus, so it is 10cm, so the green line in that triangle is<BR>\n" );
document.write( "found by the Pythagorean theorem:\r<BR>\n" );
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document.write( "  c² = a² + b²\r<BR>\n" );
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document.write( " 10² = 5² + b²\r<BR>\n" );
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document.write( " 100 = 25 + b²\r<BR>\n" );
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document.write( "  75 = b²\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2875%29 ALIGN=MIDDLE  ALT=\"sqrt%2875%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = b \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%2A3%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = b\r<BR>\n" );
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document.write( "5<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = b\r<BR>\n" );
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document.write( "So the entire diagonal is twice that or\r<BR>\n" );
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document.write( "10<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or about 17.32cm \r<BR>\n" );
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document.write( "Edwin</pre>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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