document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012965>Question 1012965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area and the perimeter of a parallelogram are 2000 sq. m. and 240 m., respectively. Find the lengths of the short and long diagonals. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629218 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=629218\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i have a problem with this problem and the problem is this.\r<BR>\n" );
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document.write( "you haven't defined what kind of parallelogram you are dealing with.<BR>\n" );
document.write( "this means that you can have several different kinds of parallelograms where the area is 2000 and the perimeter is 240.\r<BR>\n" );
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document.write( "let me explain.\r<BR>\n" );
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document.write( "area of a paraallelogram is base * height = area.\r<BR>\n" );
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document.write( "since the area is 2000, you get base * height = 2000.\r<BR>\n" );
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document.write( "perimeter of a parallelogram is 2 * base + 2 * side = perimeter.\r<BR>\n" );
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document.write( "since the perimeter is 240, you get 2 * base + 2 * side = 240.\r<BR>\n" );
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document.write( "you are dealing with 2 equations and 3 variables, so you won't get one answer.\r<BR>\n" );
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document.write( "the best you will be able to do is get one answer based on an assumption in the value of one of the other variables.\r<BR>\n" );
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document.write( "since both equations have the same base in them, we can relate these equations in terms of the base.\r<BR>\n" );
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document.write( "from the first equation, we get base = 2000 / height.\r<BR>\n" );
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document.write( "from the second equation, we get base = 120 - side.\r<BR>\n" );
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document.write( "if we substgitute 2000 / height for base in the second equation, we get:\r<BR>\n" );
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document.write( "2000 / height = 120 - side.\r<BR>\n" );
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document.write( "if we solve this equation for side, we get side = 120 - 2000 / height.\r<BR>\n" );
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document.write( "now let's look at some values that will satisfy both requirements.\r<BR>\n" );
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document.write( "the first requirement is that the area is equal to 2000.<BR>\n" );
document.write( "the second requirement is that the perimeter is equal to 240.\r<BR>\n" );
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document.write( "we will assume a height and we will then calculate the base and the side.\r<BR>\n" );
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document.write( "we will work from the following two equations.\r<BR>\n" );
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document.write( "base = 2000 / height.\r<BR>\n" );
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document.write( "side = 120 - 2000 / height.\r<BR>\n" );
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document.write( "so, we'll take some values for height and then calculate base and side and then see if the requirements of the problem are satisfied.\r<BR>\n" );
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document.write( "the following excel printout shows you what happens for values of height from 0 to 240.\r<BR>\n" );
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document.write( "see below the printout for more comments.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/011001.jpg\" alt=\"%%%\" </>\r<BR>\n" );
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document.write( "what you see from this printout is that all of the heights given and sides and bases calculated give you a parallelogram that has an area of 2000 and a perimeter of 240.\r<BR>\n" );
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document.write( "the 2 parallelograms that are rectangles have been marked.<BR>\n" );
document.write( "these are the ones where the height is equal to the side.\r<BR>\n" );
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document.write( "the other parallelograms are not rectangles, but have some angles other than 90 degrees.<BR>\n" );
document.write( "these are the ones where the height is not equal to the side.\r<BR>\n" );
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document.write( "they all, however, give you an area of 2000 and a perimeter of 240.\r<BR>\n" );
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document.write( "your question was to find the length of the long and short diagonals.\r<BR>\n" );
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document.write( "you will get several answers depending on which of these possible parallelograms is the one that you want to calculate the diagonals from.\r<BR>\n" );
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document.write( "if you meant rectangle, you will get one answer.\r<BR>\n" );
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document.write( "in other words, something is missing in the specification of the problem.\r<BR>\n" );
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document.write( "if you had given the height, then the others could have been worked out.<BR>\n" );
document.write( "if you had given the length of a side, then the others could have been worked out.\r<BR>\n" );
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document.write( "as the problem is specified, one solution is not possible.\r<BR>\n" );
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document.write( "i could be wrong, but that's my belief based on my analysis shown above.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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