document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=393628>Question 393628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> God bless you and hope you will clear my frustration to this nagging and seemingly wrong formula. We have a triangle with sides a, b and c with c as base, which is divided into two parts in r to s ratio, by altitude denoted by h. I.e. side a is hypoteneuse to r and side b to s. Is there a formula which runs as, h = [a * s  +  b * r] / r + s. Many engineers vehemently declared the wrongness of the formula<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279311 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=279311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> No, there is no such formula. A counterexample would suffice.\r<BR>\n" );
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document.write( "Let h = 1, r = 3, and s = 2.<BR>\n" );
document.write( "==> c = r + s = 5.<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+sqrt%283%5E2+%2B+1%5E2%29+=+sqrt%2810%29 ALIGN=MIDDLE  ALT=\"a+=+sqrt%283%5E2+%2B+1%5E2%29+=+sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+sqrt%282%5E2+%2B+1%5E2%29+=+sqrt%285%29 ALIGN=MIDDLE  ALT=\"b+=+sqrt%282%5E2+%2B+1%5E2%29+=+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28as+%2B+br%29%2F%28r%2Bs%29+=+%28as+%2B+br%29%2Fc+=+%282sqrt%2810%29+%2B+3sqrt%285%29%29%2F5+=+2.61 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, to 2 decimal places.  But obviously this is not equal to h = 1.  </SPAN>\n" );
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