document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199115>Question 1199115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Last question for today. \r<BR>\n" );
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document.write( "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:\r<BR>\n" );
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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: \r<BR>\n" );
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document.write( "37 = x(3x/4)\r<BR>\n" );
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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:\r<BR>\n" );
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document.write( "37 = y(9y/16)\r<BR>\n" );
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document.write( "Solving for x,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?\r<BR>\n" );
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document.write( "2. What is the correct set up for each TV to find the area?\r<BR>\n" );
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document.write( "3.  I have a hard time setting up the correct equation(s) leading to the right answer for most word problems. How can I improve my word problem-Solving skills?.\r<BR>\n" );
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document.write( "Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833035 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833035\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "We'll focus on the 4:3 tv for now.\r<BR>\n" );
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document.write( "x = length<BR>\n" );
document.write( "3x/4 = width\r<BR>\n" );
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document.write( "When you wrote<BR>\n" );
document.write( "37 = x(3x/4)<BR>\n" );
document.write( "you are implying that the area is 37 square inches since<BR>\n" );
document.write( "area = length*width\r<BR>\n" );
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document.write( "But the 37 inches refers to the length of the diagonal, and not the area.\r<BR>\n" );
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document.write( "We'll need the pythagorean theorem to tie together the length of each side, along with the diagonals. <BR>\n" );
document.write( "Notice how drawing one diagonal splits the rectangle into two congruent right triangles. <BR>\n" );
document.write( "This is why we're able to use the pythagorean theorem.\r<BR>\n" );
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document.write( "a = x = one leg<BR>\n" );
document.write( "b = 3x/4 = the other leg<BR>\n" );
document.write( "c = 37 = hypotenuse\r<BR>\n" );
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document.write( "The equation to solve is<BR>\n" );
document.write( "a^2 + b^2 = c^2<BR>\n" );
document.write( "x^2 + (3x/4)^2 = 37^2<BR>\n" );
document.write( "I'll skip the steps. You should arrive at this solution<BR>\n" );
document.write( "x = 148/5 = 29.6<BR>\n" );
document.write( "We only focus on the positive x solution.<BR>\n" );
document.write( "This decimal value is exact.\r<BR>\n" );
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document.write( "Use that x value to find 3x/4<BR>\n" );
document.write( "3x/4 = 3*29.6/4 = 22.2<BR>\n" );
document.write( "This decimal value is exact.\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "area = length*width<BR>\n" );
document.write( "area = 22.2*29.6<BR>\n" );
document.write( "area = 657.12 square inches<BR>\n" );
document.write( "This area value is exact.\r<BR>\n" );
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document.write( "=====================================================\r<BR>\n" );
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document.write( "For the 16:9 tv, we'll solve this equation<BR>\n" );
document.write( "a^2+b^2 = c^2<BR>\n" );
document.write( "y^2 + (9y/16)^2 = 37^2<BR>\n" );
document.write( "You should get this approximate positive y value<BR>\n" );
document.write( "y = 32.248295\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "9y/16 = 9*32.248295/16 = 18.139666<BR>\n" );
document.write( "This value is approximate.\r<BR>\n" );
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document.write( "Then we can compute the following:<BR>\n" );
document.write( "area = length*width<BR>\n" );
document.write( "area = 32.248295*18.139666<BR>\n" );
document.write( "area = 584.973300<BR>\n" );
document.write( "area = 584.97 square inches<BR>\n" );
document.write( "This area value is approximate.\r<BR>\n" );
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document.write( "One tip that could help with problem solving skills is to draw things out as much as possible. <BR>\n" );
document.write( "In this problem, it's recommended to draw out each rectangle. <BR>\n" );
document.write( "Then split those rectangles along one diagonal to produce the right triangles mentioned. \r<BR>\n" );
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document.write( "Another tip is to imagine you are trying to explain to somehow who isn't taking math. <BR>\n" );
document.write( "This explanation process might help you translate concepts that were previously unfamiliar.\r<BR>\n" );
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document.write( "A third tip is to keep practicing. Math is a language. <BR>\n" );
document.write( "The main way to get better at it is to keep trying to speak the language. <BR>\n" );
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