document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146037>Question 1146037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of cardboard is 12 in. longer than it is wide. Squares 3 in. on a side are to be cut from each corner, and then the sides will be folded up to make an open box with a volume of 135 in3. Find the length and width of the piece of cardboard. </SPAN>\n" );
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document.write( "The volume of the box is length times width times height.  The height is 3 inches, and the volume is 135 cubic inches.  So the length times the width is 135/3 = 45.<br><BR>\n" );
document.write( "When the 3-inch square pieces are cut out of each corner, the new length is still 12 inches more than the new width.<br><BR>\n" );
document.write( "So we can solve the problem simply by finding two numbers that differ by 12 and whose product is 45.<br><BR>\n" );
document.write( "A bit of mental arithmetic shows those two numbers to be 3 and 15.  Then, since 3-inch square pieces were cut out of each corner of the piece of cardboard, the dimensions of the piece of cardboard were 3+6=9 and 15+6=21.<br><BR>\n" );
document.write( "ANSWER: The piece of cardboard was 21x9 inches.<br><BR>\n" );
document.write( "You can, of course, solve the problem using formal algebra.<br><BR>\n" );
document.write( "x = width<BR>\n" );
document.write( "x+12 = length<br><BR>\n" );
document.write( "The volume is 135 after cutting out 3-inch squares from each corner:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-6%29%28%28x%2B12%29-6%29+=+135 ALIGN=MIDDLE  ALT=\"3%28x-6%29%28%28x%2B12%29-6%29+=+135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-6%29%28x%2B6%29+=+135 ALIGN=MIDDLE  ALT=\"3%28x-6%29%28x%2B6%29+=+135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%28x%2B6%29+=+45 ALIGN=MIDDLE  ALT=\"%28x-6%29%28x%2B6%29+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-36+=+45 ALIGN=MIDDLE  ALT=\"x%5E2-36+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+81 ALIGN=MIDDLE  ALT=\"x%5E2+=+81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9 ALIGN=MIDDLE  ALT=\"x+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "width = x = 9<BR>\n" );
document.write( "length = x+12 = 21 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );