document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102898>Question 102898</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. 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 #74853 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=74853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangle has a diagonal that is 3.6 feet longer than the length and 7.1 feet longer than the width. What are the dimensions of the rectangle?<BR>\n" );
document.write( "Let's write down what you know so far:<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=3.6+%2B+L ALIGN=MIDDLE  ALT=\"D=3.6+%2B+L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=7.1+%2B+W ALIGN=MIDDLE  ALT=\"D=7.1+%2B+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The diagonal of a rectangle also follows the Pythagorean theorem since the width and length form the sides of a right triangle with a hypotenuse that is the diagonal. Therefore,<BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2+=+L%5E2+%2B+W%5E2 ALIGN=MIDDLE  ALT=\"D%5E2+=+L%5E2+%2B+W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can use equations (1) and (2) to come up with a relationship between L and W and use that in equation (3). <BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.6%2BL ALIGN=MIDDLE  ALT=\"3.6%2BL\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.1%2BL ALIGN=MIDDLE  ALT=\"7.1%2BL\"   DISABLED_style= \"max-width:90%; height:auto;\" > are both equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then they are equal to each other. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.6%2BL=7.1%2BW ALIGN=MIDDLE  ALT=\"3.6%2BL=7.1%2BW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.6-3.6%2BL=7.1-3.6%2BW ALIGN=MIDDLE  ALT=\"3.6-3.6%2BL=7.1-3.6%2BW\"   DISABLED_style= \"max-width:90%; height:auto;\" > Additive inverse of 3.6<BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=3.5%2BW ALIGN=MIDDLE  ALT=\"L=3.5%2BW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now use equation (3) and substitute using this latest result (4) and equation (2) to get an equation that only involves the variable W. <BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2+=+L%5E2+%2B+W%5E2 ALIGN=MIDDLE  ALT=\"D%5E2+=+L%5E2+%2B+W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287.1%2BW%29%5E2=%283.5%2BW%29%5E2%2BW%5E2 ALIGN=MIDDLE  ALT=\"%287.1%2BW%29%5E2=%283.5%2BW%29%5E2%2BW%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >Substitute.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%287.1%5E2%2B2%2A7.1%2AW%2BW%5E2%29=highlight%283.5%5E2%2B2%2A3.5%2AW%2BW%5E2%29%2BW%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >Expand.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50.41%2B14.2%2AW%2BW%5E2=+12.25%2B7%2AW%2B2W%5E2 ALIGN=MIDDLE  ALT=\"50.41%2B14.2%2AW%2BW%5E2=+12.25%2B7%2AW%2B2W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify both sides. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850.41-12.25%29%2B%2814.2-7%29%2AW%2B%281-2%29W%5E2=cross%2812.25%29%2Bcross%287%2AW%29%2Bcross%282W%5E2%29-cross%2812.25%29-cross%287%2AW%29-cross%282W%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38.16%2B7.2%2AW-W%5E2=0 ALIGN=MIDDLE  ALT=\"38.16%2B7.2%2AW-W%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula to find the roots of the equation:<BR>\n" );
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;\" > <BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-1 ALIGN=MIDDLE  ALT=\"a+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+7.2 ALIGN=MIDDLE  ALT=\"b+=+7.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+38.16 ALIGN=MIDDLE  ALT=\"c+=+38.16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-7.2+%2B-+sqrt%28+7.2%5E2-4%2A%28-1%29%2A38.16+%29%29%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"W+=+%28-7.2+%2B-+sqrt%28+7.2%5E2-4%2A%28-1%29%2A38.16+%29%29%2F%282%2A%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+%28-7.2+%2B-+14.3%29%2F%28-2%29+ ALIGN=MIDDLE  ALT=\"W+=+%28-7.2+%2B-+14.3%29%2F%28-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=-3.55 ALIGN=MIDDLE  ALT=\"W=-3.55\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=10.75 ALIGN=MIDDLE  ALT=\"W=10.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > solve the equation. <BR>\n" );
document.write( "Since a negative width does not make sense, we'll only use the positive result. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=10.75 ALIGN=MIDDLE  ALT=\"W=10.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use equation (4) to get the length. <BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=3.5%2BW ALIGN=MIDDLE  ALT=\"L=3.5%2BW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=3.5%2B10.75=14.25 ALIGN=MIDDLE  ALT=\"L=3.5%2B10.75=14.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and finally <BR>\n" );
document.write( "1. D=3.6+L<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=3.6%2B14.25 ALIGN=MIDDLE  ALT=\"D=3.6%2B14.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=17.85 ALIGN=MIDDLE  ALT=\"D=17.85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can double-check your answer using the Pythagorean theorem and your length and width, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2+=+L%5E2+%2B+W%5E2 ALIGN=MIDDLE  ALT=\"D%5E2+=+L%5E2+%2B+W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2+=+14.25%5E2+%2B+10.75%5E2 ALIGN=MIDDLE  ALT=\"D%5E2+=+14.25%5E2+%2B+10.75%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2+=+203.0625+%2B+115.5625=318.625 ALIGN=MIDDLE  ALT=\"D%5E2+=+203.0625+%2B+115.5625=318.625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+17.85 ALIGN=MIDDLE  ALT=\"D+=+17.85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Good answer </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );