document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123955>Question 1123955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of the rhombus is 540 cm2; the length of one of its diagonals is 4.5 dm. What is the distance between the point of intersection of the diagonals and the side of the rhombus? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740331 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=740331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of the rhombus is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=540cm%5E2 ALIGN=MIDDLE  ALT=\"540cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; the length of one of its diagonals is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D=4.5dm=45cm ALIGN=MIDDLE  ALT=\"d%5B1%5D=4.5dm=45cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >. What is the distance between the point of intersection of the diagonals and the side of the rhombus? \r<BR>\n" );
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document.write( "Here is the rhombus with its diagonals.<BR>\n" );
document.write( "I put the rhombus inside a rectangular box for safekeeping,<BR>\n" );
document.write( "because it looked breakable. <BR>\n" );
document.write( "(I know it is not drawn to scale).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C400%2C-5.5%2C9.5%2C-3%2C3%2C%0D%0Atriangle%280%2C0%2C5%2C0%2C3.7%2C0.624%29%2Clocate%282.6%2C0.43%2Cf%29%2C%0D%0Atriangle%28-5%2C0%2C5%2C0%2C0%2C2.4%29%2Ctriangle%280%2C-2.4%2C5%2C0%2C0%2C2.4%29%2C%0D%0Aline%28-5%2C-2.4%2C5%2C-2.4%29%2Cline%28-5%2C2.4%2C5%2C2.4%29%2C%0D%0Aline%28-5%2C-2.4%2C-5%2C2.4%29%2Cline%285%2C-2.4%2C5%2C2.4%29%2C%0D%0Ared%28line%28-5%2C0%2C0%2C-2.4%29%29%2Cred%28line%285%2C0%2C0%2C-2.4%29%29%2C%0D%0Ared%28line%28-5%2C0%2C0%2C2.4%29%29%2Cred%28line%285%2C0%2C0%2C2.4%29%29%2C%0D%0Alocate%285.1%2C0.1%2C4.5dm=45cm%29%2Carrow%285.5%2C0.2%2C5.5%2C2.4%29%2C%0D%0Aarrow%285.5%2C-0.2%2C5.5%2C-2.4%29%2Clocate%28-2.55%2C0%2Cx%29%2Clocate%282.45%2C0%2Cx%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can see that the diagonals split the rhombus into4 congruent right triangles.<BR>\n" );
document.write( "Maybe you want to know the distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in cm) between the point of intersection of the diagonals and the end of the other diagonal (which is half of the length of the other diagonal).<BR>\n" );
document.write( "It is useful to calculate that length, anyway.<BR>\n" );
document.write( "The area of a rhombus is the length of one diagonal times half the length of the other.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2Ax=540 ALIGN=MIDDLE  ALT=\"45%2Ax=540\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12 ALIGN=MIDDLE  ALT=\"x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "Maybe you really wanted the distance between the point of intersection of the diagonals and the side of the rhombus, measured along the shortest path, the line perpendicular to the red side.<BR>\n" );
document.write( "That is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,the altitude to the hypotenuse of one of those right triangles.<BR>\n" );
document.write( "The length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" > of such an altitude in a right triangle with leg lengths <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and half of the other diagonal which is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D%2F2=45%2F2 ALIGN=MIDDLE  ALT=\"d%5B1%5D%2F2=45%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be found from\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff%5E2=1%2Fx%5E2%2B1%2F%28d%5B1%5D%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"1%2Ff%5E2=1%2Fx%5E2%2B1%2F%28d%5B1%5D%2F2%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=1%2Ff%5E2=1%2F12%5E2%2B1%2F22.5%5E2 ALIGN=MIDDLE  ALT=\"1%2Ff%5E2=1%2F12%5E2%2B1%2F22.5%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=1%2Ff%5E2=1%2F144%2B1%2F506.25 ALIGN=MIDDLE  ALT=\"1%2Ff%5E2=1%2F144%2B1%2F506.25\"   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=1%2Ff%5E2=%28506.25%2B144%29%2F72900 ALIGN=MIDDLE  ALT=\"1%2Ff%5E2=%28506.25%2B144%29%2F72900\"   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=1%2Ff%5E2=650.25%2F72900 ALIGN=MIDDLE  ALT=\"1%2Ff%5E2=650.25%2F72900\"   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=f%5E2=72900%2F650.25 ALIGN=MIDDLE  ALT=\"f%5E2=72900%2F650.25\"   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=f=sqrt%2872900+%2F650.25%29 ALIGN=MIDDLE  ALT=\"f=sqrt%2872900+%2F650.25%29\"   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=f=10.588 ALIGN=MIDDLE  ALT=\"f=10.588\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f=10.59%29 ALIGN=MIDDLE  ALT=\"highlight%28f=10.59%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "In other words, the distance from the center of the rhombus to one of its sides is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2810.59cm%29 ALIGN=MIDDLE  ALT=\"highlight%2810.59cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( " </SPAN>\n" );
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