document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187616>Question 187616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> jasmine drew a rectangle which is 143sqare mm. ethan drew a rectangle inside of jasmine's which is 35 square mm. ethan's rectangle has a 3 mm border between his and jasmine's rectangle. what are the length and width of jasmines rectangle?\r<BR>\n" );
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document.write( "after many attempts i believe the answer is 13mm X 11 mm. i have worked backwards but cannot seem to find the equation to use for finding either the length or width.  using A = l x w <BR>\n" );
document.write( "please help.<BR>\n" );
document.write( "donna </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140647 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=140647\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=length of outer rectangle, y=width of outer rectangle\r<BR>\n" );
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document.write( "If we draw a picture, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/rectangle.png\">\r<BR>\n" );
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document.write( "Note: the inner rectangle's dimensions are 6 units less than the corresponding on the outer rectangle since there are two 3 unit lengths per side.\r<BR>\n" );
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document.write( "Let's set up the equation for the area of the outer rectangle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=LW ALIGN=MIDDLE  ALT=\"A=LW\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the area of a rectangle formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=143=xy ALIGN=MIDDLE  ALT=\"143=xy\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=143 ALIGN=MIDDLE  ALT=\"A=143\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the area of the outer rectangle), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=x ALIGN=MIDDLE  ALT=\"L=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=y ALIGN=MIDDLE  ALT=\"W=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the dimensions of the outer rectangle)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=143%2Fx=y ALIGN=MIDDLE  ALT=\"143%2Fx=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by \"x\".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=143%2Fx ALIGN=MIDDLE  ALT=\"y=143%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "Now let's set up the equation for the area of the inner rectangle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=LW ALIGN=MIDDLE  ALT=\"A=LW\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the area of a rectangle formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35=%28x-6%29%28y-6%29 ALIGN=MIDDLE  ALT=\"35=%28x-6%29%28y-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=35 ALIGN=MIDDLE  ALT=\"A=35\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the area of the inner rectangle), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=x-6 ALIGN=MIDDLE  ALT=\"L=x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=y-6 ALIGN=MIDDLE  ALT=\"W=y-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the dimensions of the inner rectangle)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35=xy-6x-6y%2B36 ALIGN=MIDDLE  ALT=\"35=xy-6x-6y%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35=x%28143%2Fx%29-6x-6%28143%2Fx%29%2B36 ALIGN=MIDDLE  ALT=\"35=x%28143%2Fx%29-6x-6%28143%2Fx%29%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=143%2Fx ALIGN=MIDDLE  ALT=\"y=143%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35=%28143x%29%2Fx-6x-858%2Fx%2B36 ALIGN=MIDDLE  ALT=\"35=%28143x%29%2Fx-6x-858%2Fx%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35=%28143cross%28x%29%29%2Fcross%28x%29-6x-858%2Fx%2B36 ALIGN=MIDDLE  ALT=\"35=%28143cross%28x%29%29%2Fcross%28x%29-6x-858%2Fx%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35=143-6x-858%2Fx%2B36 ALIGN=MIDDLE  ALT=\"35=143-6x-858%2Fx%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35x=143x-6x%5E2-858%2B36x ALIGN=MIDDLE  ALT=\"35x=143x-6x%5E2-858%2B36x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD \"x\" to clear out the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=143x-6x%5E2-858%2B36x-35x ALIGN=MIDDLE  ALT=\"0=143x-6x%5E2-858%2B36x-35x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 35x from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-6x%5E2%2B144x-858 ALIGN=MIDDLE  ALT=\"0=-6x%5E2%2B144x-858\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-6 ALIGN=MIDDLE  ALT=\"a=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=144 ALIGN=MIDDLE  ALT=\"b=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-858 ALIGN=MIDDLE  ALT=\"c=-858\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28144%29+%2B-+sqrt%28+%28144%29%5E2-4%28-6%29%28-858%29+%29%29%2F%282%28-6%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28144%29+%2B-+sqrt%28+%28144%29%5E2-4%28-6%29%28-858%29+%29%29%2F%282%28-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-6 ALIGN=MIDDLE  ALT=\"a=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=144 ALIGN=MIDDLE  ALT=\"b=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-858 ALIGN=MIDDLE  ALT=\"c=-858\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-144+%2B-+sqrt%28+20736-4%28-6%29%28-858%29+%29%29%2F%282%28-6%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-144+%2B-+sqrt%28+20736-4%28-6%29%28-858%29+%29%29%2F%282%28-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20736 ALIGN=MIDDLE  ALT=\"20736\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-144+%2B-+sqrt%28+20736-20592+%29%29%2F%282%28-6%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-144+%2B-+sqrt%28+20736-20592+%29%29%2F%282%28-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-6%29%28-858%29 ALIGN=MIDDLE  ALT=\"4%28-6%29%28-858%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20592 ALIGN=MIDDLE  ALT=\"20592\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-144+%2B-+sqrt%28+144+%29%29%2F%282%28-6%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-144+%2B-+sqrt%28+144+%29%29%2F%282%28-6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20592 ALIGN=MIDDLE  ALT=\"20592\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20736 ALIGN=MIDDLE  ALT=\"20736\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-144+%2B-+sqrt%28+144+%29%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-144+%2B-+sqrt%28+144+%29%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-144+%2B-+12%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-144+%2B-+12%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-144+%2B+12%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-144+%2B+12%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-144+-+12%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-144+-+12%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-132%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=+%28-132%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-156%29%2F%28-12%29 ALIGN=MIDDLE  ALT=\"x+=++%28-156%29%2F%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11 ALIGN=MIDDLE  ALT=\"x+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+13 ALIGN=MIDDLE  ALT=\"x+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce \r<BR>\n" );
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document.write( "So the answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11 ALIGN=MIDDLE  ALT=\"x+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+13 ALIGN=MIDDLE  ALT=\"x+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the lengths are 11 mm or 13 mm\r<BR>\n" );
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document.write( "Since the \"length\" is usually the longer of the two measurements, let's make the length 13 mm (it doesn't matter either way).\r<BR>\n" );
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document.write( "So the width would then be...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=143%2Fx ALIGN=MIDDLE  ALT=\"y=143%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the first isolated equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=143%2F13 ALIGN=MIDDLE  ALT=\"y=143%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13 ALIGN=MIDDLE  ALT=\"x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=11 ALIGN=MIDDLE  ALT=\"y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So the width is 11 mm (note: this is the other answer)\r<BR>\n" );
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document.write( "Now subtract 6 mm from each dimension to get\r<BR>\n" );
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document.write( "13-6=7 and 11-6=5\r<BR>\n" );
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document.write( "So the inner rectangle's dimensions is 7 mm by 5 mm\r<BR>\n" );
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document.write( "Answer: \r<BR>\n" );
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document.write( "So we just found the following...\r<BR>\n" );
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document.write( "Outer Rectangle: \r<BR>\n" );
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document.write( "Length = 13 mm, Width = 11 mm\r<BR>\n" );
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document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Inner Rectangle: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Length = 7 mm, Width = 5 mm\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "143=13*11<BR>\n" );
document.write( "143=143...works\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "35=7*5<BR>\n" );
document.write( "35=35...works\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );