document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152809>Question 1152809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Donatello starts with a marble cube of side length 10. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length s. Find s.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774912 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=774912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let x be the distance from a corner of the cube to where the cut is made to slice off each pyramid.  Then the length of each side of the new polyhedron is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Each side of the original cube is then made up of two segments of length x and one of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+2x%2Bx%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"10+=+2x%2Bx%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+x%282%2Bsqrt%282%29%29 ALIGN=MIDDLE  ALT=\"10+=+x%282%2Bsqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10%2F%282%2Bsqrt%282%29%29+=+10%282-sqrt%282%29%29%2F2+=+5%282-sqrt%282%29%29+=+10-5sqrt%282%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The side length s of the new polyhedron is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Asqrt%282%29+=+%2810-5sqrt%282%29%29%2Asqrt%282%29+=+10sqrt%282%29-10+=+10%28sqrt%282%29-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );