document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530769>Question 530769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 68cm. If the diagonal is 26cm, 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 #350210 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=350210\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> perimeter = 2(a +b), where a = length and b = width<BR>\n" );
document.write( "p = 68<BR>\n" );
document.write( "a+b = 34<BR>\n" );
document.write( "so<BR>\n" );
document.write( "a = 34-b<BR>\n" );
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document.write( "diagonal = c = 26 cm<BR>\n" );
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document.write( "Pythagorean Theorem teaches us that:<BR>\n" );
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document.write( "c^2 = a^2 + b^2<BR>\n" );
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document.write( "Substitute for a = 34-b and c = 26<BR>\n" );
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document.write( "26^2  = (34-b)^2 + b^2<BR>\n" );
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document.write( "Collect terms.<BR>\n" );
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document.write( "676 = (b^2 -68b + 1156) + b^2<BR>\n" );
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document.write( "2b^2 -68b + 480 = 0<BR>\n" );
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document.write( "b^2 -34b +240 = 0<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28500%2C500%2C-20%2C40%2C-60%2C40%2Cx%5E2-34%2Ax%2B240%29+ ALIGN=MIDDLE  ALT=\"+graph%28500%2C500%2C-20%2C40%2C-60%2C40%2Cx%5E2-34%2Ax%2B240%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Factor<BR>\n" );
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document.write( "(b-10)(b-24) = 0<BR>\n" );
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document.write( "b = 10 or 24<BR>\n" );
document.write( "a = 34 -b<BR>\n" );
document.write( "so <BR>\n" );
document.write( "a = 24 or 10 respectively<BR>\n" );
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document.write( "Either way, the two sides of the rectangle are 10 and 24.<BR>\n" );
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document.write( "Checking, we find:<BR>\n" );
document.write( "10^2 + 24^2 = 26^2<BR>\n" );
document.write( "100 + 576 = 676<BR>\n" );
document.write( "True<BR>\n" );
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document.write( "Answer: The rectangle has dimensions of 10 by 24 cm.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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