document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=944289>Question 944289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 7 inches and the width is 4 inches. If both the length and width are increased by equal amounts, the area is increased by 42 square inches. Find the length and width of the larger rectangle.\r<BR>\n" );
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document.write( "I am so confused! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575760 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=575760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "you start with a length of 7 and a width of 4.<BR>\n" );
document.write( "the area is length * width which is equal to 7 * 4 = 28\r<BR>\n" );
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document.write( "when you increase the length and the width by the same amount, the area is increased by 42.\r<BR>\n" );
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document.write( "let the amount that you are increasing the length and width by be equal to x.\r<BR>\n" );
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document.write( "the new length is 4 + x.<BR>\n" );
document.write( "the new width is 7 + x\r<BR>\n" );
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document.write( "since the original area is 28, and you increase it by 42, the new area must be equal to 70.\r<BR>\n" );
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document.write( "since length * width = area, you get:\r<BR>\n" );
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document.write( "(4 + x) * (7 + x) = 70\r<BR>\n" );
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document.write( "this can also be written as:\r<BR>\n" );
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document.write( "(x + 4) * (x + 7) = 70\r<BR>\n" );
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document.write( "multiply out the factors to get:\r<BR>\n" );
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document.write( "x^2 + 11x + 28 = 70\r<BR>\n" );
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document.write( "subtract 70 from both sides of the equation to get:\r<BR>\n" );
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document.write( "x^2 + 11x - 42 = 0\r<BR>\n" );
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document.write( "this is a quadratic equation that is in standard form.\r<BR>\n" );
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document.write( "factor it to get:\r<BR>\n" );
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document.write( "(x + 14) * (x - 3) = 0\r<BR>\n" );
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document.write( "solve for x to get x = -14 or x = 3\r<BR>\n" );
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document.write( "x can't be negative so the solution is x = 3\r<BR>\n" );
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document.write( "now go back to the original equation to see if you did this right.\r<BR>\n" );
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document.write( "with the original measurements, the area is equal to 7 * 4 = 28\r<BR>\n" );
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document.write( "when you add 3 to the length and you add 3 to the width, and you add 42 to the area, you get:\r<BR>\n" );
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document.write( "(7 + 3) * (4 + 3) = 28 + 42 which becomes 10 * 7 = 70 which becomes 70 = 70.\r<BR>\n" );
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document.write( "since this is a true statement, the value of 3 for x is confirmed as correct.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "the length of the larger rectangle is 10.<BR>\n" );
document.write( "the width of the larger rectangle is 7.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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