document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=223774>Question 223774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 60cm. If the length is decreased by 5 and the width is halved, the perimeter will decrease by 20cm. What are the length and width of the original rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167270 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 60cm. If the length is decreased by 5 and the width is halved, the perimeter will decrease by 20cm. What are the length and width of the original rectangle?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 1.  Perimeter P means adding up all 4 sides of a rectangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2.  Let w be the original width.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3.  Let L be the original length.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 4.  Let w/2 be the width cut in half\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  Let L-5 be the length reduced by 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 6.  Then, original perimeter P0=L+L+w+w=2L+2w=60\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 7.  Then, new perimeter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P1=L-5%2BL-5%2Bw%2F2%2Bw%2F2=2L%2Bw-10=60-20=40 ALIGN=MIDDLE  ALT=\"P1=L-5%2BL-5%2Bw%2F2%2Bw%2F2=2L%2Bw-10=60-20=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2Bw=50 ALIGN=MIDDLE  ALT=\"2L%2Bw=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > after adding 10 to both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 8.  Our linear system of equation is given in Steps 6 and 7 as\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2B2w=60 ALIGN=MIDDLE  ALT=\"2L%2B2w=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L%2Bw=50 ALIGN=MIDDLE  ALT=\"2L%2Bw=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++2%5CL+%2B+2%5Cw+=+60%2C%0D%0A++++2%5CL+%2B+1%5Cw+=+50+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5CL+%2B+2%5Cw+=+60%2C%0D%0A++++2%5CL+%2B+1%5Cw+=+50+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 2*w to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2AL+=+60+-+2%2Aw ALIGN=MIDDLE  ALT=\"2%2AL+=+60+-+2%2Aw\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+60%2F2+-+2%2Aw%2F2 ALIGN=MIDDLE  ALT=\"L+=+60%2F2+-+2%2Aw%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%2860%2F2+-+2%2Aw%2F2%29+%2B+1%5Cw+=+50 ALIGN=MIDDLE  ALT=\"2%2A%2860%2F2+-+2%2Aw%2F2%29+%2B+1%5Cw+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that w=10. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+60%2F2+-+2%2Aw%2F2 ALIGN=MIDDLE  ALT=\"L+=+60%2F2+-+2%2Aw%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, L=20.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+L=20%2C+w=10+%29 ALIGN=MIDDLE  ALT=\"system%28+L=20%2C+w=10+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=20 ALIGN=MIDDLE  ALT=\"L=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=10 ALIGN=MIDDLE  ALT=\"w=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  And <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P0=2%2820%2B10%29=60 ALIGN=MIDDLE  ALT=\"P0=2%2820%2B10%29=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P1=+2%2A20%2B10-10=40 ALIGN=MIDDLE  ALT=\"P1=+2%2A20%2B10-10=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > which are true statements.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 5.  ANSWER:  The width is 10 cm and the length is 20 cm.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope the above steps were helpful.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Good luck in your studies!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Respectfully,<BR>\n" );
document.write( "Dr J<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );