document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=796887>Question 796887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A  monument consists of two cubical blocks, the smaller resting on the larger. The total height of the mmonument is 5 feet, and the area of the exposed surface is 61 square feet. Find the dimensions of the blocks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #481602 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=481602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Drawing a little picture, you can see that, on the bottom block, you can see 4 complete faces of the cube presuming you would actually be able to walk around it.  If we let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e_1\"> represent the measure of the edge of the larger cube, then the surface area of each of the faces that can be seen in their entirety is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e_1^{\,2} \">, so the total of those areas is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 4e_1^{\,2}\">.  The top block, which edge we will refer to as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e_2\">, has the four sides and the top visible, so that part is represented by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5e_2^{\,2}\">.  That leaves the partially exposed top face of the bottom block to account for.  If the top cube wasn't there, the exposed area of the top face of the bottom block would be simply <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e_1^{\,2} \">, but since it is partly covered by an area that amounts to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e_2^{\,2} \">, the actual visible area is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e_1^{\,2}\ -\ e_2^{\,2} \">.  Putting the whole thing together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(e_1^{\,2}\ -\ e_2^{\,2}\right)\ +\  4e_1^{\,2}\ +\ 5e_2^{\,2}\ =\ \ 61\">.\r<BR>\n" );
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document.write( "Which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5e_1^{\,2}\ +\ 4e_2^{\,2}\ =\ \ 61\">.\r<BR>\n" );
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document.write( "Finally, since the total height of the stack is 5 feet:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ e_1\ +\ e_2\ =\ 5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ e_2\ =\ 5\ -\ e_1 \">\r<BR>\n" );
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document.write( "Substituting:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5e_1^{\,2}\ +\ 4\left(5\ -\ e_1\right)^{\,2}\ =\ \ 61\">.\r<BR>\n" );
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document.write( "The only thing left for you to do is to expand the binomial, collect like terms, put the quadratic in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e_1\"> into standard form, and solve.  Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e_1\"> represents the edge of the larger cube and the height is 5, the edge of the larger cube has to be larger than 2.5 feet.  Hence, if you get a root that is smaller than 2.5 feet (and you will get one given correct arithmetic), discard it.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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