document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062239>Question 1062239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have a painting that is 30 in. wide and 22.5 in. tall. You would like to reproduce it <BR>\n" );
document.write( "on a sheet of paper that measures 8 1/2 in. by 11 in., leaving at least a 1­in. margin on <BR>\n" );
document.write( "all four sides. a) What scale should you use if you keep the sheet of paper in the <BR>\n" );
document.write( "normal upright orientation? Assume that the reproduction will be as large as possible. <BR>\n" );
document.write( "b) What scale should you use if you turn the paper on its side? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677166 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the painting is 22.5 inches tall and 30 inches wide.\r<BR>\n" );
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document.write( "when the paper is vertically oriented, it is 11 inches tall and 8.5 inches wide.<BR>\n" );
document.write( "take away 1 inch border and the usable dimensions would be 9 inches tall and 8.5 inches wide.\r<BR>\n" );
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document.write( "if you use the height as the controlling ratio, then the scale factor would be 9/22.5.\r<BR>\n" );
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document.write( "22.5 inches tall * 9/22.5 = 9 inches tall.<BR>\n" );
document.write( "30 inches wide * 9/22.5 = 12 inches wide.\r<BR>\n" );
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document.write( "the ratio of height to width is preserved since 22.5/30 = .75 and 9/12 = .75.\r<BR>\n" );
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document.write( "however, the 12 inches width is greater than the 6.5 inches width allowed, so this doesn't work.\r<BR>\n" );
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document.write( "if you use the width as the controlling ratio, then the scale factor would be 6.5/30.\r<BR>\n" );
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document.write( "22.5 inches tall * 6.5/30 = 4.875 inches tall.<BR>\n" );
document.write( "30 inches wide * 6.5/30 = 6.5 inches wide.\r<BR>\n" );
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document.write( "the ratio of height to width is preserved since 22.5/30 = .75 and 4.875/6.5 = .75\r<BR>\n" );
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document.write( "both height and width are now within the outer limits of 9 inches tall and 6.5 inches wide, so these measurements are good and the scale factor is 6.5/30 which is equivalent to 13/60 is you want it in rational number form.\r<BR>\n" );
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document.write( "you would do similar analysis when the paper is horizontally oriented.\r<BR>\n" );
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document.write( "you would find that the height is now the controlling factor and the scale factor would be 6.5/22.5.\r<BR>\n" );
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document.write( "you would get a height on the paper of 22.5 * 6.5/22.5 = 6.5.<BR>\n" );
document.write( "you would get a width on the paper of 30 * 6.5/22.5 = 8.67.\r<BR>\n" );
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document.write( "the height to width ratio on the paper would be .75, same as on the painting, and the height and width limits on the paper would be adhered to:\r<BR>\n" );
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document.write( "they are less than or equal to 6.5 inches on the height and less than or equal to 9 inches on the width.\r<BR>\n" );
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document.write( "so, to the best of my knowledge, your solutions would be:\r<BR>\n" );
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document.write( "scale factor of 6.5/30 = 13/60 if the paper is vertically oriented.\r<BR>\n" );
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document.write( "scale factor of 6.5/22.5 = 13/45 is the paper is horizontally oriented.\r<BR>\n" );
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