document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187757>Question 1187757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangular wood is 5cm more the twice height and its width is five times the height.\r<BR>\n" );
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document.write( "What is the dimensions of the wood if its volume is 180cm³?\r<BR>\n" );
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document.write( "What is the length of the wood if its volume is 495cm³? </SPAN>\n" );
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document.write( "Let x = height<br><BR>\n" );
document.write( "Then from the given information<br><BR>\n" );
document.write( "2x+5 = length<BR>\n" );
document.write( "5x = width<br><BR>\n" );
document.write( "The volume is length times width times height:<br><BR>\n" );
document.write( "V = x(2x+5)(5x)<br><BR>\n" );
document.write( "or<br><BR>\n" );
document.write( "V = 10x^3+25x^2<br><BR>\n" );
document.write( "We are to find x and thus the dimensions if the volume is 180, and if the volume is 495.<br><BR>\n" );
document.write( "One way to find the answers would be to solve the equations 10x^3+25x^2=180 and 10x^3+25x^2=495.  But solving a cubic equation is mostly a matter of trial and error.<br><BR>\n" );
document.write( "A much easier method, since the given volumes are whole numbers, is to look for whole number values of x which make the product (x)(2x+5)(5x) equal to 180 or 495.<br><BR>\n" );
document.write( "Clearly x has to be small; so we can just try x=1, 2, 3... to find the answers.<br><BR>\n" );
document.write( "x=1: (x)(2x+5)(5x) = (1)(7)(5) = 35<BR>\n" );
document.write( "x=2: (x)(2x+5)(5x) = (2)(9)(10) = 180<BR>\n" );
document.write( "x=3: (x)(2x+5)(5x) = (3)(11)(15) = 495<br><BR>\n" );
document.write( "We have found both the required volumes....<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "volume 180 cm^3: dimensions 2cm by 9cm by 10cm<BR>\n" );
document.write( "volume 495 cm^3: dimensions 3cm by 11cm by 15cm<br><BR>\n" );
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