document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209114>Question 1209114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box has a certain length, width, and height.  The length of the box is equal to twice its width, as well as equal to 8 less than its height.  If the total surface area of the box is 480, then what is the height of the box? </SPAN>\n" );
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document.write( "Answer: <BR>\n" );
document.write( "exact height = 5 + sqrt(129)<BR>\n" );
document.write( "approximate height = 16.357816691601\r<BR>\n" );
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document.write( "Work Shown\r<BR>\n" );
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document.write( "\"length is twice the width\" ---> \"width is half the length\".<BR>\n" );
document.write( "\"length is 8 units smaller than the height\" ---> \"height is 8 units longer compared to length\".<BR>\n" );
document.write( "x = length<BR>\n" );
document.write( "x/2 = 0.5x = width<BR>\n" );
document.write( "x+8 = height\r<BR>\n" );
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document.write( "S = surface area of the box<BR>\n" );
document.write( "S = 2*(length*width + length*height + width*height)<BR>\n" );
document.write( "480 = 2*(x*0.5x + x*(x+8) + 0.5x*(x+8))<BR>\n" );
document.write( "480 = 2*(0.5x^2 + x^2+8x + 0.5x^2+4x)<BR>\n" );
document.write( "480 = 2*(2x^2 +12x)<BR>\n" );
document.write( "480 = 4x^2 +24x<BR>\n" );
document.write( "4x^2+24x-480 = 0<BR>\n" );
document.write( "4(x^2+6x-120) = 0<BR>\n" );
document.write( "x^2+6x-120 = 0/4<BR>\n" );
document.write( "x^2+6x-120 = 0\r<BR>\n" );
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document.write( "Plug a = 1, b = 6, c = -120 into the quadratic formula.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2B-sqrt%28129%29 ALIGN=MIDDLE  ALT=\"x+=+-3%2B-sqrt%28129%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8.357816691601 ALIGN=MIDDLE  ALT=\"x+=+8.357816691601\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-14.357816691601 ALIGN=MIDDLE  ALT=\"x+=+-14.357816691601\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Ignore the negative x value. <BR>\n" );
document.write( "A negative length makes no sense.<BR>\n" );
document.write( "Each decimal value mentioned is approximate.<BR>\n" );
document.write( "Round it however your teacher instructs.\r<BR>\n" );
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document.write( "Add 8 to the length to find the height.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=height+=+x%2B8+=+-3%2Bsqrt%28129%29%2B8+=+5%2Bsqrt%28129%29+=+16.357816691601 ALIGN=MIDDLE  ALT=\"height+=+x%2B8+=+-3%2Bsqrt%28129%29%2B8+=+5%2Bsqrt%28129%29+=+16.357816691601\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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