document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=814968>Question 814968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is 4 cm2<BR>\n" );
document.write( " while its perimeter is 10 cm. Find the dimensions of the <BR>\n" );
document.write( "rectangle.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #490626 by </B><A HREF=/tutors/aboutme.mpl?userid=FightinBlueHens><B>FightinBlueHens(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=FightinBlueHens><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=490626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. First let's start with the information that you know. <BR>\n" );
document.write( "2. We need to represent this information to solve it.<BR>\n" );
document.write( "3. We will represent this information in 2 equations. Start with what you know.<BR>\n" );
document.write( "4. We know we are dealing with a rectangle, and the area of a rectangle can be represented by width x height. We're going to call the width the base<BR>\n" );
document.write( "5. Let the base=x, and the height=y so the formula for the area is x*y=4.<BR>\n" );
document.write( "6. We know that the perimeter of a rectangle is equal to the the length of all 4 sides, so two times the height plus 2 times the base. This can be represented by 2x+2y= 10 (because we know that the perimeter equals 10).\r<BR>\n" );
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document.write( "First you need to solve for one variable, so let's start with the problem 2x+2y=10.\r<BR>\n" );
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document.write( "2x+2y=10.\r<BR>\n" );
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document.write( "2y=10-2x  (Here you move the term 2x to the opposite side by subtracting it from one side, and then doing the same thing to the other side.)\r<BR>\n" );
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document.write( "2y/2=(10/2)-(2x/2) You want just the variable (y) on one side so divide both sides by 2.\r<BR>\n" );
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document.write( "y=5-x  Now you know what y equals, so you can plug this variable in to the first equation.\r<BR>\n" );
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document.write( "x*y=4 --> x*(5-x)=4\r<BR>\n" );
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document.write( "5x-x^2=4 Distribute.\r<BR>\n" );
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document.write( "-x^2+5x-4=0 Bring all the terms to one side so you can solve for x, and write the equation in standard form so that you can solve it more easily.\r<BR>\n" );
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document.write( "(-x+1)(x-4)=0 Factor the equation \r<BR>\n" );
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document.write( "Here there are two possible answers.\r<BR>\n" );
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document.write( "[(-x+1)(x-4)]/(x-4)=0/(x-4) Divide both sides by x-4 to figure out one of the answers.\r<BR>\n" );
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document.write( "-x+1=0  This is the answer to dividing both sides by x-4\r<BR>\n" );
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document.write( "-x=-1 Subtract 1 from both sides.\r<BR>\n" );
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document.write( "x=1 Multiply both sides by negative one to find out the positive value of x. This is a positive number, that can be one answer to your problem.\r<BR>\n" );
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document.write( "Do the other side\r<BR>\n" );
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document.write( "[(-x+1)(x-4)]/(-x+1)= 0/(-x+1) Divide (-x+1)(x-4)=0 by (-x+1) on both sides to solve for (x-4)\r<BR>\n" );
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document.write( "x-4=0\r<BR>\n" );
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document.write( "x=4\r<BR>\n" );
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document.write( "Your answers are x=1 and x=4.  Now plug these answers back into the original equation xy=4.\r<BR>\n" );
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document.write( "4y=4\r<BR>\n" );
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document.write( "y=1 Divide both sides by 4.\r<BR>\n" );
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document.write( "1y=4\r<BR>\n" );
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document.write( "y=4 (Divide both sides by 1)\r<BR>\n" );
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document.write( "1 and 4 can be in the place of x or y because they give you the same answer.\r<BR>\n" );
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document.write( "As for the perimeter 2x+2y=10:\r<BR>\n" );
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document.write( "2*4+2*1= 8+2\r<BR>\n" );
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document.write( "8+2=10 (This's the perimeter.)\r<BR>\n" );
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