document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171116>Question 1171116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi\r<BR>\n" );
document.write( "\n" );
document.write( "Andrew was given a rectangular cardboard 28cm by 16cm. How many right angle triangles 4cm high base 3cm could cut out. \r<BR>\n" );
document.write( "\n" );
document.write( "Thanks\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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 #796015 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52782)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Andrew was given a rectangular cardboard 28cm by 16cm. How many right angle triangles 4cm high base 3cm could cut out.<BR>\n" );
document.write( "~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Two right angled triangles with the legs of 3 cm and 4 cm, placed hypotenuse to hypotenuse, form a 3x4-rectangle.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let's calculate how many such rectangles can be placed onto the 28x16 cm cardboard.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We have two basic placements.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "One placement is to direct the 4-cm side of the rectangle along its 28 cm dimension.\r\n" );
document.write( "\r\n" );
document.write( "By doing this way, we have 28/4 = 7 rectanles in this direction and, OBVIOSLY, 5 rectangles in the perpendicular direction,\r\n" );
document.write( "                                                     (because 16/3 = 5.33 = 5 when rounded to the closest smaller integer).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In all, we have 7*5 = 35 rectangles and, hence, 35*2 = 70 right angled triangles at such placement.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, consider another placement, directing the 4-cm side side along the 16-cm side of the cardboard.\r\n" );
document.write( "\r\n" );
document.write( "We have then the 3-cm side along the 28-cm side of the cardboard.\r\n" );
document.write( "\r\n" );
document.write( "By doing this way, we have 4 rectangles along the 16-cm side of the cardboard and, OBVIOUSLY, 9 rectangles along its 28 cm side \r\n" );
document.write( "                                                               (because 28/3 = 9.33 = 9 rounded to the closest smaller integer).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In all, we have 4*9 = 36 rectangles and, hence, 36*2 = 72 right angled triangles at such placement.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Of these two opportunities, we chose the placement, which gives maximum numer of rectangles (36) and maximum number of triangles (72).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "<U>ANSWER</U>.  Maximum number of triangles is 72.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Such problems teachers give to young &nbsp;(advanced ?) &nbsp;students of &nbsp;5th - 6th &nbsp;grades to check if they are able <BR>\n" );
document.write( "to think on self-standing basis and to teach them to solve such problems accurately &nbsp;(and to think accurately) <BR>\n" );
document.write( "on the self-standing manner.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The solution by &nbsp;@MathLover1, &nbsp;based on consideration the areas &nbsp;ONLY, &nbsp;gives an &nbsp;ESTIMATION &nbsp;ONLY <BR>\n" );
document.write( "for the maximum number of triangles from the top, &nbsp;but does not give the exact number of triangles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The solution by &nbsp;@MathLover1 &nbsp;IS &nbsp;NOT &nbsp;what is expected.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Learn on how to solve such problems &nbsp;(and how to teach your students, &nbsp;if you are a teacher) - from my post.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );