document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016731>Question 1016731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The scale of a map is 1:20 000. Find the area on the map which represents 124km squared.\r<BR>\n" );
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document.write( "Thanks so much! How do you do this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #633127 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=633127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it's important to know what the measurements are on the map versus what the measurements are in the real world.\r<BR>\n" );
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document.write( "you are told that the area is 124 square kilometers in real life.\r<BR>\n" );
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document.write( "the scale on the map says 1 something on the map is equal to 20,000 somethings in real life.\r<BR>\n" );
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document.write( "it's probably a centimeter on the map is equal to 20,000 meters in real life, although that's just a guess.\r<BR>\n" );
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document.write( "assuming the guess is correct, you would find the area on the map in the following manner.\r<BR>\n" );
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document.write( "20,000 meters is equal to 20 kilometers.\r<BR>\n" );
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document.write( "that means that 1 centimeter on the map is equal to 20 kilometers in real life.\r<BR>\n" );
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document.write( "that's a linear measurement.\r<BR>\n" );
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document.write( "the area on the map would be 1 * 1 = 1 square meter.\r<BR>\n" );
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document.write( "the corresponding area in the real world would be 20 * 20 = 400 square kilometers.\r<BR>\n" );
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document.write( "the scale on the map can therefore be translated as follows:\r<BR>\n" );
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document.write( "1 centimeter on the map equals 20 kilometers in the real world.\r<BR>\n" );
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document.write( "1 square centimeter on the map equals 400 square kilometers in the real world.\r<BR>\n" );
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document.write( "your real world measurements are 124 square kilometers.\r<BR>\n" );
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document.write( "your translation factors is 1 / 400 = x / 124\r<BR>\n" );
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document.write( "that says that 1 square centimeter on the map divided by 400 square kilometers in the real world is the same ratio as 2 square centimeters on the map divided by 124 square kilometers in the real world.\r<BR>\n" );
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document.write( "you would cross multiply to get 1 * 124 = 400 * x\r<BR>\n" );
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document.write( "you would solve for x to get x = (1 * 124) / 400 = .31 square centimeters on the map.\r<BR>\n" );
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document.write( "this says that .31 square centimeters on the map is equal to 124 square kilometers in the real world.\r<BR>\n" );
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document.write( "if you give your area in the world world some dimensions, this might be easier to see.\r<BR>\n" );
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document.write( "assume that 124 square kilometers is a strip of land 10 kilometers by 12.4 kilometers in the real world.\r<BR>\n" );
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document.write( "10 * 12.4 = 124 square kilometers.\r<BR>\n" );
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document.write( "the scale on the map is 1:20,000 which we have assumed is 1 centimeter to 20,000 meters, which we have translated to 1 centimeter to 20 kilometers.\r<BR>\n" );
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document.write( "the area in the real world is 10 kilometers by 12.4 kilometers.\r<BR>\n" );
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document.write( "the scale on the map says 1 centimeter on the map is equal to 20 kilometers in the real world.\r<BR>\n" );
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document.write( "a scale of 1:20 means that the measurement on the map is 1/20 * the measurement in the real world, and the measurement on the map is centimeters while the measurement in the real world is kilometers.\r<BR>\n" );
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document.write( "a distance of 10 kilometers in the real world is therefore equal to 1/20 * 10 = .5 centimeters on the map.\r<BR>\n" );
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document.write( "a distance of 12.4 kilometers in the real world is therefore equal to 1/20 * 12.4 = .62 centimeters on the map.\r<BR>\n" );
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document.write( "the dimensions in the real world are 10 kilometers by 12.4 kilometers.<BR>\n" );
document.write( "the dimensions on the map are .5 centimeters by .62 centimeters.\r<BR>\n" );
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document.write( "the area in the real world is 10 * 12.4 = 124 square kilometers.<BR>\n" );
document.write( "the area on the map is .5 * .62 = .31 centimeters.\r<BR>\n" );
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document.write( "the numbers check out so the logic looks good.\r<BR>\n" );
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document.write( "what remains to be determined is what the actual measurements are on the map versus the actual measurements in the real world.\r<BR>\n" );
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document.write( "i've assumed kilometers in the real world.<BR>\n" );
document.write( "i guessed at centimeters on the map.\r<BR>\n" );
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document.write( "you can double check to see what they really are.<BR>\n" );
document.write( "if they are different, then you'd need to change your analysis accordingly.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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