document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075076>Question 1075076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of the rhombus is 480 cm2; the length of one of its diagonals is 4.8 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 #689774 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=689774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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%2C4.8dm=48cm%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;\" ><BR>\n" );
document.write( "You can see that the diagonals split the rhombus into<BR>\n" );
document.write( "4 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)<BR>\n" );
document.write( "between the point of intersection of the diagonals and<BR>\n" );
document.write( "the end of the other diagonal<BR>\n" );
document.write( "(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<BR>\n" );
document.write( "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=48%2Ax=480 ALIGN=MIDDLE  ALT=\"48%2Ax=480\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Maybe you really wanted the distance between the point of intersection of the diagonals and the side of the rhombus,<BR>\n" );
document.write( "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;\" > ,<BR>\n" );
document.write( "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<BR>\n" );
document.write( "in a right triangle with leg lengths <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "can be found from<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff%5E2=1%2Fa%5E2%2B1%2Fb%5E2 ALIGN=MIDDLE  ALT=\"1%2Ff%5E2=1%2Fa%5E2%2B1%2Fb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In this case,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff%5E2=1%2F10%5E2%2B1%2F24%5E2=1%2F100%2B1%2F576=%28576%2B100%29%2F57600=676%2F57600=4%2A169%2F%284%2A25%2A576%29=169%2F%2825%2A576%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff%5E2=169%2F%2825%2A576%29 ALIGN=MIDDLE  ALT=\"1%2Ff%5E2=169%2F%2825%2A576%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E2=25%2A576%2F169 ALIGN=MIDDLE  ALT=\"f%5E2=25%2A576%2F169\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f=sqrt%2825%2A576%29%2Fsqrt%28169%29=5%2A24%2F13 ALIGN=MIDDLE  ALT=\"f=sqrt%2825%2A576%29%2Fsqrt%28169%29=5%2A24%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f=120%2F13%29 ALIGN=MIDDLE  ALT=\"highlight%28f=120%2F13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In other words, the distance from the center of the rhombus<BR>\n" );
document.write( "to one of its sides is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289.23cm%29 ALIGN=MIDDLE  ALT=\"highlight%289.23cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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