document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1060021>Question 1060021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 3 inches longer than it is wide. If the area is 70 square inches, what are 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 #675057 by </B><A HREF=/tutors/aboutme.mpl?userid=acw1213><B>acw1213(28)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=acw1213><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=acw1213><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=675057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We need to write a system of equations here.\r<BR>\n" );
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document.write( "One equation will include the formula for the area/<BR>\n" );
document.write( "The formula for the area of a rectangle is<BR>\n" );
document.write( "Lw = a\r<BR>\n" );
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document.write( "where\r<BR>\n" );
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document.write( "L = length<BR>\n" );
document.write( "W = width<BR>\n" );
document.write( "a = area\r<BR>\n" );
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document.write( "Plug in the area where it is necessary.\r<BR>\n" );
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document.write( "Lw = 70\r<BR>\n" );
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document.write( "One equation is finished!\r<BR>\n" );
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document.write( "The next equation will be the situation described in your response.\r<BR>\n" );
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document.write( "The length is 3 inches added to the width.\r<BR>\n" );
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document.write( "In an equation, it is\r<BR>\n" );
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document.write( "3 + w = L\r<BR>\n" );
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document.write( "Now use your systems,\r<BR>\n" );
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document.write( "3 + w = L<BR>\n" );
document.write( "Lw = 70\r<BR>\n" );
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document.write( "to solve for the length and width.\r<BR>\n" );
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document.write( "I'm going to solve using substitution.\r<BR>\n" );
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document.write( "Substitute 3 + w in for \"L\" in the second equation.\r<BR>\n" );
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document.write( "(3 + w)(w)=70\r<BR>\n" );
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document.write( "Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w+%2B+w%5E2+=+70 ALIGN=MIDDLE  ALT=\"3w+%2B+w%5E2+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have a quadratic equation on our hands. Let's get this into standard form.\r<BR>\n" );
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document.write( "Subtract 70 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w+%2B+w%5E2+-+70+=+0 ALIGN=MIDDLE  ALT=\"3w+%2B+w%5E2+-+70+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We cannot factor this, so solve using the quadratic formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a = 3<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "c = -70\r<BR>\n" );
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document.write( "Plug in and solve for w.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A3%2A-70+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A3%2A-70+%29%29%2F%282%2A3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify. Please view my steps.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-1+%2B-+sqrt%28+1%2B840+%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-1+%2B-+sqrt%28+1%2B840+%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I squared 1 and multiplied -4 by 3, and then by -70.<BR>\n" );
document.write( "I multiplied 2 times 3. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-1+%2B-+sqrt%28841%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-1+%2B-+sqrt%28841%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I added one to 840.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-1+%2B-+29%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-1+%2B-+29%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I found the square root of 841, which is 29.\r<BR>\n" );
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document.write( "Now, we need to solve for \"w\". -1 can be ADDED or SUBTRACTED from 29, so we need to solve for both\r<BR>\n" );
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document.write( "Addition:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-1+%2B+29%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-1+%2B+29%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-1 + 29 is 28.<BR>\n" );
document.write( "28 / 6 can be simplified to 14/3.\r<BR>\n" );
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document.write( "w = 14/3\r<BR>\n" );
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document.write( "Subtraction:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-1+-+29%29%29%2F%286%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-1+-+29%29%29%2F%286%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-1 - 29 is -30.<BR>\n" );
document.write( "-30 / 6 is -5.\r<BR>\n" );
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document.write( "w = -5\r<BR>\n" );
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document.write( "Now we have a problem. w can equal -5 or 14/3.<BR>\n" );
document.write( "-5 is the more logical answer since 14/3 will turn out to be a repeating decimal.\r<BR>\n" );
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document.write( "Our width is -5.\r<BR>\n" );
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document.write( "Don't worry, our system is not old news yet!<BR>\n" );
document.write( "Let's return to it.\r<BR>\n" );
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document.write( "Lw = 70<BR>\n" );
document.write( "w + 3 = L<BR>\n" );
document.write( "Let's plug in -5 for \"w\" in the second equation and solve for \"L\".\r<BR>\n" );
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document.write( "-5 + 3 = L\r<BR>\n" );
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document.write( "-5 + 3 is -2.\r<BR>\n" );
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document.write( "-2 = L\r<BR>\n" );
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document.write( "YAY! We are finished!<BR>\n" );
document.write( "Our width is -5 and our length is -2. These are our DIMENSIONS. </SPAN>\n" );
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