document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065330>Question 1065330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 42cm. if the diagonal is 15cm find the width 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 #680491 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=680491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> l,w = length, width, respectively<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++2l%2B2w+=+42+ ALIGN=MIDDLE  ALT=\"++2l%2B2w+=+42+\"   DISABLED_style= \"max-width:90%; height:auto;\" >    (1)<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28l%5E2%2Bw%5E2%29+=+15+ ALIGN=MIDDLE  ALT=\"+sqrt%28l%5E2%2Bw%5E2%29+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (2)\r<BR>\n" );
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document.write( "(1) —> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+w+=+21+ ALIGN=MIDDLE  ALT=\"l+%2B+w+=+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" > —> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+l+=+21-w+ ALIGN=MIDDLE  ALT=\"+l+=+21-w+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Square both sides of (2):<BR>\n" );
document.write( "          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+l%5E2+%2B+w%5E2+=+225+ ALIGN=MIDDLE  ALT=\"+l%5E2+%2B+w%5E2+=+225+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now substitute \"21-w\" for \"l\"  in this last expression:<BR>\n" );
document.write( "          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2821-w%29%5E2+%2B+w%5E2+=+225+ ALIGN=MIDDLE  ALT=\"+%2821-w%29%5E2+%2B+w%5E2+=+225+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28441-21w-21w%2Bw%5E2%29+%2B+w%5E2+=+225+ ALIGN=MIDDLE  ALT=\"+%28441-21w-21w%2Bw%5E2%29+%2B+w%5E2+=+225+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms, and rearrange:<BR>\n" );
document.write( "          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++2w%5E2+-+42w+%2B+216+=+0+ ALIGN=MIDDLE  ALT=\"++2w%5E2+-+42w+%2B+216+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide through by 2:<BR>\n" );
document.write( "          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++w%5E2+-+21w+%2B+108+=+0+ ALIGN=MIDDLE  ALT=\"++w%5E2+-+21w+%2B+108+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "          <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28w-9%29%28w-12%29+=+0+ ALIGN=MIDDLE  ALT=\"++%28w-9%29%28w-12%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "       w = 9  or w = 12\r<BR>\n" );
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document.write( "If w = 9, (1) tells us l = 12<BR>\n" );
document.write( "if w = 12, (1) tells us l = 9   (<<< discard because convention is l>w for a rectangle)\r<BR>\n" );
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document.write( "—<BR>\n" );
document.write( "Ans:<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+length+=+12cm%29 ALIGN=MIDDLE  ALT=\"+highlight%28+length+=+12cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28width+=+9cm+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28width+=+9cm+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "—<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "      Diagonal = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%5E2+%2B+9%5E2%29+=+sqrt%28144%2B81%29+=+sqrt%28225%29+=+15+ ALIGN=MIDDLE  ALT=\"sqrt%2812%5E2+%2B+9%5E2%29+=+sqrt%28144%2B81%29+=+sqrt%28225%29+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (ok)<BR>\n" );
document.write( "      Perimeter = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2l%2B2w+=+2%2812%29+%2B+2%289%29+=+24%2B18+=+42+ ALIGN=MIDDLE  ALT=\"+2l%2B2w+=+2%2812%29+%2B+2%289%29+=+24%2B18+=+42+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ok)   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );