document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1070239>Question 1070239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Paul put some rectangular paintings on the wall. For each picture he<BR>\n" );
document.write( "put one nail into the wall 2.5 m above the floor and attached a 2 m<BR>\n" );
document.write( "long string at the two upper corners. Which of the following pictures is<BR>\n" );
document.write( "closest to the floor (format: width in cm × height in cm)?<BR>\n" );
document.write( "A) 60×40 B) 120×50 C) 120×90 D) 160×60 E) 160×100<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #685356 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=685356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "convert meters to centimeters and you have .....\r<BR>\n" );
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document.write( "nail is 250 cm above the floor.<BR>\n" );
document.write( "string is 200 cm long.\r<BR>\n" );
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document.write( "to be balanced, 100 cm of the string will be on the left and 100 cm of the string will be on the right.\r<BR>\n" );
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document.write( "these 100 cm lengths will form the hypotenuse of a right triangle that has its horizontal leg equal to 1/2 the width of the picture.\r<BR>\n" );
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document.write( "the other leg of the right triangle formed will be the vertical leg which forms the distance between the nail and the top of the picture.\r<BR>\n" );
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document.write( "pythagorus formula is:\r<BR>\n" );
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document.write( "c^2 = a^2 + b^2\r<BR>\n" );
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document.write( "c is the hypotenuse.<BR>\n" );
document.write( "a is the vertical leg which is the distance between the nail in the wall and the top of the picture.<BR>\n" );
document.write( "b is the horizontal leg which is equal to 1/2 the width of the picture.\r<BR>\n" );
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document.write( "solve for a to get:\r<BR>\n" );
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document.write( "a = sqrt(c^2 - b^2)\r<BR>\n" );
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document.write( "since c = 100, the formula becomes a = sqrt(100^2 - b^2)\r<BR>\n" );
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document.write( "b will be either 30 or 60 or 80.\r<BR>\n" );
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document.write( "30 is half of the width of the picture whose width is 60.<BR>\n" );
document.write( "60 is half of the width of the picture whose width is 120.<BR>\n" );
document.write( "80 is half of the width of the picture whose width is 160.\r<BR>\n" );
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document.write( "to solve for a, you get:\r<BR>\n" );
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document.write( "when b = 30, a = sqrt(100^2 - 30^2) = 95.4<BR>\n" );
document.write( "when b = 60, a = sqrt(100^2 - 60^2) = 80<BR>\n" );
document.write( "when b = 80, a = sqrt(100^2 - 80^2) = 60\r<BR>\n" );
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document.write( "these are all measurements in cm.\r<BR>\n" );
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document.write( "that gets you the distance from the top of each picture to the nail.\r<BR>\n" );
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document.write( "now you have to add the length of each picture to see which picture is closest to the floor.\r<BR>\n" );
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document.write( "the picture with width of 60 has a longest height of 40, so the distance between the bottom of that picture and the nail is equal to 95.4 + 40 = 135.4 cm.\r<BR>\n" );
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document.write( "the picture with width of 120 has a longest height of 90, so the distance between the bottom of that picture and the nail is equal to 80 + 90 = 170 cm.\r<BR>\n" );
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document.write( "the picture with width of 160 has a longest height of 100, so the distance between the bottom of that picture and the nail is equal to 60 + 100 = 160 cm.\r<BR>\n" );
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document.write( "the distance from the nail to the floor is 250 cm.\r<BR>\n" );
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document.write( "250 - 135.4 = 114.6 cm.<BR>\n" );
document.write( "250 - 170 = 80 cm.<BR>\n" );
document.write( "250 - 160 = 90 cm.\r<BR>\n" );
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document.write( "the picture that hangs closest to the floor would be the picture that is 120 cm wide and 90 cm high.\r<BR>\n" );
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document.write( "i believe that's going to be selection C.\r<BR>\n" );
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document.write( "here's a picture of the calculations for the longest height of each.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/022501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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