document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002096>Question 1002096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been stuck to this question on my math exam..can you solve this for me?\r<BR>\n" );
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document.write( "Find the dimension of a rectangle with an area of 27 square meters, if the length of a rectangle is three more than twice the width.\r<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 #619089 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=619089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> area of a rectangle = length * width\r<BR>\n" );
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document.write( "the length is equal to 3 more than twice the width.\r<BR>\n" );
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document.write( "the equation for that is:\r<BR>\n" );
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document.write( "length = 2 * width + 3\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "area = length * width\r<BR>\n" );
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document.write( "replace length with 2 * width + 3 to get:\r<BR>\n" );
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document.write( "area = (2 * width + 3) * width\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "area = 2 * width^2 + 3 * width\r<BR>\n" );
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document.write( "since the area = 27, then replace area with 27 to get:\r<BR>\n" );
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document.write( "27 = 2 * width^2 + 3 * width\r<BR>\n" );
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document.write( "subtract 27 from both sides of this equation to get:\r<BR>\n" );
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document.write( "0 = 2 * width^2 + 3 * width - 27\r<BR>\n" );
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document.write( "this is the same aqs:\r<BR>\n" );
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document.write( "2 * width^2 + 3 * width - 27 = 0\r<BR>\n" );
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document.write( "this equation is in standard form of ax^2 + bx + c = 0.\r<BR>\n" );
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document.write( "replace width with x and your equation becomes:\r<BR>\n" );
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document.write( "2x^2 + 3x - 27 = 0\r<BR>\n" );
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document.write( "now it's easier to see that your equation is in the standard form of ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "since it is in standard form, you can find a and b and c.\r<BR>\n" );
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document.write( "a is the coefficient of the x^2 term.<BR>\n" );
document.write( "b is the coefficient of the x term.<BR>\n" );
document.write( "c is the constant term.\r<BR>\n" );
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document.write( "in your equation of 2x^2 + 3x - 27 = 0, you get:\r<BR>\n" );
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document.write( "a = 2<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "c = -27\r<BR>\n" );
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document.write( "don't forget that you made x = width.<BR>\n" );
document.write( "you will need that fact later on.\r<BR>\n" );
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document.write( "to factor the equation of 2x^2 + 3x - 27 = 0, use the quadratic formula.\r<BR>\n" );
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document.write( "the quadratic formula says that:\r<BR>\n" );
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document.write( "x = (-b + or - sqrt(b^2-4ac)) / (2a)\r<BR>\n" );
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document.write( "this results in 2 possible answers.\r<BR>\n" );
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document.write( "x = (-b + sqrt(b^2-4ac))/(2a) or:<BR>\n" );
document.write( "x = (-b - sqrt(b^2-4ac))/(2a)\r<BR>\n" );
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document.write( "when a = 2 and b = 3 and c = -27, you get:\r<BR>\n" );
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document.write( "b^2 = 3^2 = 9\r<BR>\n" );
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document.write( "4ac = 4*2*-27) = -216\r<BR>\n" );
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document.write( "b^2-4ac = 9-(-216) = 9+216 = 225\r<BR>\n" );
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document.write( "sqrt(b^2-4ac) = sqrt(225) = 15\r<BR>\n" );
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document.write( "-b = -3\r<BR>\n" );
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document.write( "2a = 4\r<BR>\n" );
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document.write( "x = (-b + sqrt(b^2-4ac))/(2a) or:<BR>\n" );
document.write( "x = (-b - sqrt(b^2-4ac))/(2a) becomes:\r<BR>\n" );
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document.write( "x = (-3 + 15)/4 or:<BR>\n" );
document.write( "x = (-4 - 15)/4 which becomes:\r<BR>\n" );
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document.write( "x = 3 or:<BR>\n" );
document.write( "x = -4.5\r<BR>\n" );
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document.write( "since x can't be negative, you are left with:\r<BR>\n" );
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document.write( "x = 3\r<BR>\n" );
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document.write( "now's the time to remember that x represents the width.\r<BR>\n" );
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document.write( "go back to your original equation that said:\r<BR>\n" );
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document.write( "27 = length * width\r<BR>\n" );
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document.write( "since width = 3, this equation becomes 27 = length * 3\r<BR>\n" );
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document.write( "solve for length to get length = 9.\r<BR>\n" );
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document.write( "you have length = 9 and width = 3\r<BR>\n" );
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document.write( "now's the time to confirm your solution satisfies the problem requirements.\r<BR>\n" );
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document.write( "those are:\r<BR>\n" );
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document.write( "Find the dimension of a rectangle with an area of 27 square meters, if the length of a rectangle is three more than twice the width.\r<BR>\n" );
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document.write( "you found the dimensions.\r<BR>\n" );
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document.write( "they are length = 9 and width = 3.\r<BR>\n" );
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document.write( "an additional requirement is that length is equal to three more than twice the width.\r<BR>\n" );
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document.write( "the width is 3.\r<BR>\n" );
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document.write( "twice the width is 6\r<BR>\n" );
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document.write( "length is 9 which is 3 more than 6.\r<BR>\n" );
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document.write( "length is 3 more than twice the width so you have met that requirement.\r<BR>\n" );
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document.write( "you're solution is good.\r<BR>\n" );
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document.write( "the dimensions are:\r<BR>\n" );
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document.write( "length = 9<BR>\n" );
document.write( "width = 3\r<BR>\n" );
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document.write( " </SPAN>\n" );
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