document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204562>Question 1204562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ms. R wants to construct a house for her pet bunny out of a cardboard box. To make the house she is going to cut squares of side length x cm from each corner of a rectangular box (see diagram below). The original dimensions of the uncut box are 51 cm by 45 cm. She wants the volume of the house to be 7175 cm^3.\r<BR>\n" );
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document.write( "Here is the link to the image: https://gyazo.com/b09d71efd4ffcfcc851e1ad3c3821622\r<BR>\n" );
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document.write( "a) Determine an equation that models this situation.<BR>\n" );
document.write( "b) Find all possible dimensions of the box. </SPAN>\n" );
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document.write( "The piece of cardboard is 51 x 45 cm, and squares with sides x are cut out of each corner.  The dimensions of the bottom of the box are then 51-2x and 45-2x; and the height of the box is x.<br><BR>\n" );
document.write( "Then the volume is length times width times height: V = (x)(51-2x)(45-2x)<br><BR>\n" );
document.write( "We want that volume to be 7175 cubic centimeters.<br><BR>\n" );
document.write( "ANSWER a):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2851-2x%29%2845-2x%29=7175 ALIGN=MIDDLE  ALT=\"%28x%29%2851-2x%29%2845-2x%29=7175\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "or<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3-192x%5E2%2B2295x=7175 ALIGN=MIDDLE  ALT=\"4x%5E3-192x%5E2%2B2295x=7175\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graphing calculator will show that there are two solutions; but with one of them the box is very deep with a much smaller base, making it not a good solution.  That solution is also an irrational number, making finding the solution difficult without something like a graphing calculator.<br><BR>\n" );
document.write( "For finding the reasonable solution, the easiest way is by looking at the factors of 7175.  The difference in the dimensions of the cardboard is 6 cm, so we need to find factors of 7175 that differ by 6.<br><BR>\n" );
document.write( "7175 = 25(287) = (5)(5)(7)(41) = (5)(35)(41)<br><BR>\n" );
document.write( "This tells us that the squares cut out of each corner have side lengths of 5 cm, and the dimensions of the bottom of the box are 35 x 41 cm.<br><BR>\n" );
document.write( "ANSWER b): 5 x 35 x 41 cm<br><BR>\n" );
document.write( "or (approximately) 11.3265 x 22.347 x 28.347 cm<br><BR>\n" );
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