document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208776>Question 1208776</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 a 4:3 format, meaning the ratio of the length to the width of the screen is 4 to 3.\r<BR>\n" );
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document.write( "A. What is the area of a 37-inch traditional TV screen?\r<BR>\n" );
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document.write( "B. What is the area of a 37-inch LCD TV whose screen is in a 16 : 9 format?\r<BR>\n" );
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document.write( "Hint given in textbook:\r<BR>\n" );
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document.write( "If x is the length of a 4 : 3 format screen, then (3/4)(x) is the width. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847226 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=847226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part A\r<BR>\n" );
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document.write( "If you were to use that hint, then you'll have this diagram.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-4%2C4%2C-3%2C3%2C%0D%0Aline%28-3%2C-2%2C3%2C-2%29%2Cline%283%2C-2%2C3%2C2%29%2Cline%283%2C2%2C-3%2C2%29%2Cline%28-3%2C2%2C-3%2C-2%29%2Cline%28-3%2C-2%2C3%2C2%29%2C%0D%0Alocate%28-0.48%2C0.34%2C%2237%22%29%2Clocate%28-0.62%2C-2.22%2B0.15%2C%22x%22%29%2Clocate%283.26-0.2%2C0.26%2C%22%283%2F4%29x%22%29%2C%0D%0Alocate%28-3.5-0.3%2C-2.6%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The diagonal splits the rectangle into two congruent right triangles.<BR>\n" );
document.write( "Use the Pythagorean Theorem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to form this equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28+%283%2F4%29x+%29%5E2+=+37%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28+%283%2F4%29x+%29%5E2+=+37%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a sub-goal is to solve for x.<BR>\n" );
document.write( "I'll leave the scratch work for the student to do. <BR>\n" );
document.write( "You should find the two solutions to that equation are x = 148/5 and x = -148/5<BR>\n" );
document.write( "Ignore the negative x value since we cannot have a negative width.\r<BR>\n" );
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document.write( "x = 148/5 = 29.6<BR>\n" );
document.write( "(3/4)x = (3/4)*(148/5) = 111/5 = 22.2<BR>\n" );
document.write( "For a 37 inch TV to have a 4:3 aspect ratio, the screen needs to be 29.6 inches across horizontally and 22.2 inches tall.<BR>\n" );
document.write( "Note that (29.6)^2+(22.2)^2 = 37^2 due to the Pythagorean Theorem.<BR>\n" );
document.write( "The area of this TV is therefore 29.6*22.2 = 657.12 square inches.\r<BR>\n" );
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document.write( "Another approach for part A\r<BR>\n" );
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document.write( "The use of a fraction in (3/4)x is a bit clunky in my opinion. <BR>\n" );
document.write( "We can avoid that fraction by letting 4x be the horizontal portion of the screen and 3x be the vertical height, as shown here,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-4%2C4%2C-3%2C3%2C%0D%0Aline%28-3%2C-2%2C3%2C-2%29%2Cline%283%2C-2%2C3%2C2%29%2Cline%283%2C2%2C-3%2C2%29%2Cline%28-3%2C2%2C-3%2C-2%29%2Cline%28-3%2C-2%2C3%2C2%29%2C%0D%0Alocate%28-0.48%2C0.34%2C%2237%22%29%2Clocate%28-0.62%2C-2.22%2B0.15%2C4x%29%2Clocate%283.26-0.2%2C0.26%2C3x%29%2C%0D%0Alocate%28-3.5-0.3%2C-2.6%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note the ratio 4x:3x reduces to 4:3\r<BR>\n" );
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document.write( "If you were to solve <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;\" > you would get x = -37/5, x = 37/5 as the two solutions. We ignore the negative solution.\r<BR>\n" );
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document.write( "horizontal = 4x = 4*37/5 = 148/5 = 29.6 inches<BR>\n" );
document.write( "vertical = 3x = 3*37/5 = 111/5 = 22.2 inches<BR>\n" );
document.write( "area = 29.6*22.2 = 657.12 square inches.\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "This is one possible diagram to draw, when having a 16:9 screen<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-4%2C4%2C-3%2C3%2C%0D%0Aline%28-3%2C-2%2C3%2C-2%29%2Cline%283%2C-2%2C3%2C2%29%2Cline%283%2C2%2C-3%2C2%29%2Cline%28-3%2C2%2C-3%2C-2%29%2Cline%28-3%2C-2%2C3%2C2%29%2C%0D%0Alocate%28-0.48%2C0.34%2C%2237%22%29%2Clocate%28-0.62%2C-2.22%2B0.15%2C16x%29%2Clocate%283.26-0.2%2C0.26%2C9x%29%2C%0D%0Alocate%28-3.5-0.3%2C-2.6%2Cmatrix%281%2C4%2C%22Diagram%22%2C%22not%22%2C%22to%22%2C%22scale%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The length of the diagonal is the same as before.<BR>\n" );
document.write( "The equation to solve would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x%29%5E2%2B%289x%29%5E2+=+37%5E2 ALIGN=MIDDLE  ALT=\"%2816x%29%5E2%2B%289x%29%5E2+=+37%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The positive solution from this equation is x = 37*sqrt(337)/337<BR>\n" );
document.write( "That would approximate to roughly x = 2.01551843<BR>\n" );
document.write( "area = 16x*9x = 16*2.01551843*9*2.01551843 = 584.973294000432<BR>\n" );
document.write( "This is roughly a 584.97 square inch screen depending how you round that decimal value.<BR>\n" );
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