document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249403>Question 249403</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagonal of a television set is 52 inches long. Its length is 28 inches more than its height. Find the dimensions of the television set. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181666 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=181666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diagonal of the TV can be considered the hypotenuse of a right triangle.  It can be solved using the Pythagorean formula:  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5E2+=+A%5E2+%2B+B%5E2 ALIGN=MIDDLE  ALT=\"C%5E2+=+A%5E2+%2B+B%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Assuming L is the width of the TV set, which the problem calls \"length\", and H is the height of the screen.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+H+%2B+28 ALIGN=MIDDLE  ALT=\"L+=+H+%2B+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Returning to the Pythagorean formula...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+diagonal+=+52 ALIGN=MIDDLE  ALT=\"D+=+diagonal+=+52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2+=+L%5E2+%2B+H%5E2 ALIGN=MIDDLE  ALT=\"D%5E2+=+L%5E2+%2B+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substituting L = H+28<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2+=+%28H%2B28%29%5E2+%2B+H%5E2 ALIGN=MIDDLE  ALT=\"D%5E2+=+%28H%2B28%29%5E2+%2B+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52%5E2+=+%28H%2B28%29%28H%2B28%29+%2B+H%5E2 ALIGN=MIDDLE  ALT=\"52%5E2+=+%28H%2B28%29%28H%2B28%29+%2B+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52%5E2+=+H%5E2+%2B+28H+%2B+28H+%2B+784+%2B+H%5E2 ALIGN=MIDDLE  ALT=\"52%5E2+=+H%5E2+%2B+28H+%2B+28H+%2B+784+%2B+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52%5E2+=+2H%5E2+%2B+56H+%2B+784 ALIGN=MIDDLE  ALT=\"52%5E2+=+2H%5E2+%2B+56H+%2B+784\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Squaring 52<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2704+=+2H%5E2+%2B+56H+%2B+784 ALIGN=MIDDLE  ALT=\"2704+=+2H%5E2+%2B+56H+%2B+784\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Dividing both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1352+=+H%5E2+%2B+28H+%2B+392 ALIGN=MIDDLE  ALT=\"1352+=+H%5E2+%2B+28H+%2B+392\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtracting 1352 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+H%5E2+%2B+28H+%2B+392+-+1352 ALIGN=MIDDLE  ALT=\"0+=+H%5E2+%2B+28H+%2B+392+-+1352\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Simplifying<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+H%5E2+%2B+28H+-960 ALIGN=MIDDLE  ALT=\"0+=+H%5E2+%2B+28H+-960\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Can 960 be factored such that the two terms are 28 apart?<BR>\n" );
document.write( "Yes.  48*20 = 960 and 48-20=28<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28H%2B48%29%28H-20%29+=+0 ALIGN=MIDDLE  ALT=\"%28H%2B48%29%28H-20%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So we have two candidate solutions:  H= -48 and H = 20.  Since a negative height is nonsense, then our suggested answer is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+20 ALIGN=MIDDLE  ALT=\"H+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Looking back to our defined equations, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+H+%2B+28+=+20+%2B+28+=+48 ALIGN=MIDDLE  ALT=\"L+=+H+%2B+28+=+20+%2B+28+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Checking by using the Pythagorean formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+52 ALIGN=MIDDLE  ALT=\"D+=+52\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+=+48%5E2+=+2304 ALIGN=MIDDLE  ALT=\"L%5E2+=+48%5E2+=+2304\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2+=+20%5E2+=+400 ALIGN=MIDDLE  ALT=\"H%5E2+=+20%5E2+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+%2B+H%5E2+=+2704 ALIGN=MIDDLE  ALT=\"L%5E2+%2B+H%5E2+=+2704\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282704%29+=+52 ALIGN=MIDDLE  ALT=\"sqrt%282704%29+=+52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So that checks just fine.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "But is it an analog TV or an HDTV?<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Analog TV has a ratio of width to height of 4:3.  The picture is 4 units wide by 3 units high.<BR>\n" );
document.write( "HDTV has a ration of 16:9.  The picture is 16 units wide by 9 units high.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Our proposed TV set has a picture that is 48 wide by 20 high.  That is a ratio of 48:20, or 24:10, or 12:5.  This does not correspond to any real TV set.  So perhaps a negative height would work when solving an \"imaginary\" TV problem. Hmmm... </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );