document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199532>Question 1199532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is 21 cm square. If one side exceeds the other by 4 cm, Find the dimensions of the rectangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833461 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>3 cm by 7 cm rectangle</font><BR>\n" );
document.write( "3*7 = 21\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Let's list the ways to factor 21 with positive values:<BR>\n" );
document.write( "1*21 = 21<BR>\n" );
document.write( "3*7 = 21\r<BR>\n" );
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document.write( "The gap from 3 to 7 is 4 units, because 7-3 = 4, so it's fairly clear that we have a 3 by 7 rectangle.\r<BR>\n" );
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document.write( "Another approach using algebra.\r<BR>\n" );
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document.write( "x = width<BR>\n" );
document.write( "x+4 = length which is four units larger than the width\r<BR>\n" );
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document.write( "area = length*width<BR>\n" );
document.write( "area = (x+4)*x<BR>\n" );
document.write( "area = x^2+4x\r<BR>\n" );
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document.write( "We'll set this equal to the stated area 21 square cm, and solve for x.\r<BR>\n" );
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document.write( "x^2+4x = 21<BR>\n" );
document.write( "x^2+4x-21 = 0\r<BR>\n" );
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document.write( "From here you can factor like so<BR>\n" );
document.write( "x^2+4x-21 = 0<BR>\n" );
document.write( "(x-3)(x+7) = 0<BR>\n" );
document.write( "x-3 = 0 or x+7 = 0<BR>\n" );
document.write( "x = 3 or x = -7<BR>\n" );
document.write( "Ignore x = -7 because it makes no sense to have a negative length or width.\r<BR>\n" );
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document.write( "If x = 3, then x+4 = 3+4 = 7<BR>\n" );
document.write( "We arrive at 3*7 = 21 to confirm the answers.\r<BR>\n" );
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document.write( "Another way to solve x^2+4x-21 = 0 is to use the quadratic formula.<BR>\n" );
document.write( "We have<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 4<BR>\n" );
document.write( "c = -21<BR>\n" );
document.write( "to get the following steps:<BR>\n" );
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document.write( "Then as mentioned earlier, we ignore the negative x value and have x = 3 lead to x+4 = 7.<BR>\n" );
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