document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=584744>Question 584744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A TV screen is 40in high and 60in long.  Using the vetical and horizontal control buttons, the picture is compressed to 62.5% of its original area, leaving a uniform dark strip around the outside.  Find the dimensions of the smaller picture. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372877 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=372877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> original dimensions are 40 * 60 for an area of 2400 square inches.<BR>\n" );
document.write( "the area is reduced to 62.5% of its original area.<BR>\n" );
document.write( "this makes the near area equal to .625 * 2400 = 1500.<BR>\n" );
document.write( "if we let x equal the height and y equal the length, then we get:<BR>\n" );
document.write( "x * y = 1500<BR>\n" );
document.write( "since we know that the length to height ratio is 60/40 = 3/2, we can set the length equal to 3/2 * the height.<BR>\n" );
document.write( "since x equals the height and y equals the length, this means that:<BR>\n" );
document.write( "y = 3/2 * x<BR>\n" );
document.write( "in our equation of x * y = 1500, we replace y with 3/2 * x to get:<BR>\n" );
document.write( "x * 3/2 * x = 1500 which simplifies to:<BR>\n" );
document.write( "3/2 * x^2 = 1500<BR>\n" );
document.write( "multiply both sides of this equation by 2/3 to get:<BR>\n" );
document.write( "x^2 = 1500 * 2/3 which simplifies to:<BR>\n" );
document.write( "x^2 = 1000.<BR>\n" );
document.write( "solve for x to get x = 31.6227766<BR>\n" );
document.write( "since x = 31.6227766, and y = 3/2 * x, we can solve for y to get:<BR>\n" );
document.write( "y = 3/2 * 31.6227766 which is equal to:<BR>\n" );
document.write( "y = 47.4341649<BR>\n" );
document.write( "we now have the new dimensions of the screen assuming the same viewing ratio as the original screen.<BR>\n" );
document.write( "those new dimensions are:<BR>\n" );
document.write( "height = 47.4341649 inches<BR>\n" );
document.write( "width = 31.6227766<BR>\n" );
document.write( "the new area is equal to height * width which is equal to:<BR>\n" );
document.write( "47.4341649 * 31.6227766 which is equal to 1500 square inches, confirming the calculations are correct.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );