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" );
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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" );
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document.write( "Thanks\r<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 #796013 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</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=796013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor is certainly not correct.  You can't determine the number of triangles simply by dividing the area of the whole sheet of cardboard by the area of one of the triangles.  When you actually cut out the triangles, there will (with the given dimensions of the piece of cardboard) be some cardboard that can't be cut into triangles.<br><BR>\n" );
document.write( "Two of the right triangles together make up a 3x4 rectangle.  If one dimension of the original cardboard were a multiple of 4 and the other a multiple of 3, then all the cardboard could be cut into the triangles.<br><BR>\n" );
document.write( "But neither of the given dimensions is a multiple of 3; so there will be some cardboard that can't be used to make the triangles.<br><BR>\n" );
document.write( "Both dimensions are multiples of 4.<br><BR>\n" );
document.write( "Consider the number of 3x4 rectangles we can make from a piece of cardboard that is 28x16.<br><BR>\n" );
document.write( "(1) If the long dimension of each small rectangle is in the same direction as the LONGER dimension of the piece of cardboard, then we can get 28/4 = 7 rectangles in that direction.  Then we could get 16/3 = 5 rectangles (remember it has to be a whole number) in the other direction.  That would give us 7*5=35 rectangles, each consisting of 2 of the triangles, for a total of 70 triangles.<br><BR>\n" );
document.write( "(2) If the long dimension of each small rectangle is in the same direction as the SHORTER dimension of the piece of cardboard, then we can get 16/4 = 4 rectangles in that direction.  Then we could get 28/3 = 9 rectangles (remember it has to be a whole number) in the other direction.  That would give us 4*9=36 rectangles, each consisting of 2 of the triangles, for a total of 72 triangles.<br><BR>\n" );
document.write( "So the latter method of cutting the triangles from the piece of cardboard gives us more triangles.<br><BR>\n" );
document.write( "It is remotely possible, however, that some unusual arrangement of the triangles on the piece of cardboard would allow us to squeeze out one or even two more triangles; so we can't be completely sure of our answer.<br><BR>\n" );
document.write( "ANSWER: A maximum of 72 right triangles with height 4cm and base 3cm can be cut from a piece of cardboard that is 28cm by 16cm.<br><BR>\n" );
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