document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199156>Question 1199156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The screen size of a television is determined by the length of the diagonal of the rectangular screen. Traditional TVs come in 4 : 3 format, meaning the ratio of the length to the width of the rectangular screen is 4 to 3. What is the area of a 37-inch Traditional TV screen? What is the area of a 37-inch LCD TV whose screen is in a 16 : 9 format? Which screen is larger?\r<BR>\n" );
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document.write( "Hint given but the textbook:<BR>\n" );
document.write( "If x is the length of a 4 : 3 format screen, then (3x/4)is the width.\r<BR>\n" );
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document.write( "Let me see.\r<BR>\n" );
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document.write( "I know what x represents. I will say let y = length of a 16 : 9 format screen. If this is true, then 9y/16 is the width.\r<BR>\n" );
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document.write( "My set up for x goes like this:<BR>\n" );
document.write( "37 = x(3x/4)<BR>\n" );
document.write( "Solving for x, I get 7.024.\r<BR>\n" );
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document.write( "My set up for y goes like this:<BR>\n" );
document.write( "37 = y(9y/16)<BR>\n" );
document.write( "Solving for y,I get 8.11035.\r<BR>\n" );
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document.write( "I see that y > x,meaning the LCD TV screen format is bigger.<BR>\n" );
document.write( "However, according to the textbook,I am wrong.\r<BR>\n" );
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document.write( "Textbook Answer:\r<BR>\n" );
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document.write( "The screen of a 37-inch TV in 4 : 3 format has an area of 657.12 in^2.<BR>\n" );
document.write( "The screen of a 37-inch TV in 16 : 9 format has an area of 587.97 in^2.<BR>\n" );
document.write( "According to the textbook, the traditional TV has the bigger screen.\r<BR>\n" );
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document.write( "Questions:\r<BR>\n" );
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document.write( "1. What did I do wrong?<BR>\n" );
document.write( "2. What is the correct set up for each TV to find the area?<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832868 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832868\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here are the equations you are trying to use to solve the problem:<br><BR>\n" );
document.write( "(1) 37 = x(3x/4)<BR>\n" );
document.write( "(2) 37 = y(9y/16)<br><BR>\n" );
document.write( "Those equations both say (incorrectly!) that the length of the diagonal is the product of the length and width.<br><BR>\n" );
document.write( "That of course is not true; the length of the diagonal is found using the Pythagorean Theorem: (length) squared plus (width) squared equals (diagonal) squared.<br><BR>\n" );
document.write( "NOTE: While your textbook suggests using x and (3/4)x for the dimensions of the traditional TV screen, I would prefer to use 4x and 3x -- why introduce fractions into our calculations when not necessary?  I will do that in my response below.<br><BR>\n" );
document.write( "Traditional TV, dimensions 3x and 4x....<br><BR>\n" );
document.write( "The length of the diagonal is 37 inches:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%5E2%2B%284x%29%5E2=37%5E2 ALIGN=MIDDLE  ALT=\"%283x%29%5E2%2B%284x%29%5E2=37%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2%2B16x%5E2=1369 ALIGN=MIDDLE  ALT=\"9x%5E2%2B16x%5E2=1369\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2=1369 ALIGN=MIDDLE  ALT=\"25x%5E2=1369\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1089%2F25=54.76 ALIGN=MIDDLE  ALT=\"x%5E2=1089%2F25=54.76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The area of the screen is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%284x%29=12x%5E2=12%2854.76%29=657.12 ALIGN=MIDDLE  ALT=\"%283x%29%284x%29=12x%5E2=12%2854.76%29=657.12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That matches the answer in your textbook.<br><BR>\n" );
document.write( "LCD TV, dimensions 9x and 16x....<br><BR>\n" );
document.write( "The length of the diagonal is 37 inches:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%29%5E2%2B%2816x%29%5E2=37%5E2 ALIGN=MIDDLE  ALT=\"%289x%29%5E2%2B%2816x%29%5E2=37%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81x%5E2%2B256x%5E2=37%5E2 ALIGN=MIDDLE  ALT=\"81x%5E2%2B256x%5E2=37%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=337x%5E2=1369 ALIGN=MIDDLE  ALT=\"337x%5E2=1369\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1369%2F337=4.0623 ALIGN=MIDDLE  ALT=\"x%5E2=1369%2F337=4.0623\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to 4 decimal places)<br><BR>\n" );
document.write( "The area of the screen is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%29%2816x%29=144x%5E2=584.97 ALIGN=MIDDLE  ALT=\"%289x%29%2816x%29=144x%5E2=584.97\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<br><BR>\n" );
document.write( "That doesn't quite match what you show as the answer in your textbook.  Perhaps you didn't show the textbook answer correctly...?<br><BR>\n" );
document.write( "The bottom line is that the area of the traditional TV screen is greater.<br><BR>\n" );
document.write( " </SPAN>\n" );
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