document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182199>Question 182199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions of a rectangle that has an area 48 m^2 and a diagonal of length 10 m. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136726 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=136726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the length of the rectangle and y = the width of the rectangle.<BR>\n" );
document.write( "The area is x*y = 48 sq.m.<BR>\n" );
document.write( "The diagonal is 10 m, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the Pythagorean theorem.<BR>\n" );
document.write( "So we have two equations:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay+=+48 ALIGN=MIDDLE  ALT=\"x%2Ay+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite this equation as: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+48%2Fy ALIGN=MIDDLE  ALT=\"x+=+48%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substitute into equation 2).<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2+=+100 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2848%2Fy%29%5E2%2By%5E2+=+100 ALIGN=MIDDLE  ALT=\"%2848%2Fy%29%5E2%2By%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying this, we get:<BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304%2Fy%5E2+%2B+y%5E2+=+100 ALIGN=MIDDLE  ALT=\"2304%2Fy%5E2+%2B+y%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282304+%2B+y%5E4%29%2Fy%5E2+=+100 ALIGN=MIDDLE  ALT=\"%282304+%2B+y%5E4%29%2Fy%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304+%2B+y%5E4+=+100y%5E2 ALIGN=MIDDLE  ALT=\"2304+%2B+y%5E4+=+100y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange this into standard \"quadratic\" form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4-100y%5E2%2B2034+=+0 ALIGN=MIDDLE  ALT=\"y%5E4-100y%5E2%2B2034+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve by factoring, noting that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4+=+%28y%5E2%29%5E2 ALIGN=MIDDLE  ALT=\"y%5E4+=+%28y%5E2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%29%5E2+-+100%28y%5E2%29%2B2304+=+0 ALIGN=MIDDLE  ALT=\"%28y%5E2%29%5E2+-+100%28y%5E2%29%2B2304+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%5E2%29-64%29%28%28y%5E2%29-36%29+=+0 ALIGN=MIDDLE  ALT=\"%28%28y%5E2%29-64%29%28%28y%5E2%29-36%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Applying the zero product rule, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-64+=+0 ALIGN=MIDDLE  ALT=\"y%5E2-64+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-36+=+0 ALIGN=MIDDLE  ALT=\"y%5E2-36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factoring the left sides, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B8%29%28y-8%29+=+0 ALIGN=MIDDLE  ALT=\"%28y%2B8%29%28y-8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B6%29%28y-6%29+=+0 ALIGN=MIDDLE  ALT=\"%28y%2B6%29%28y-6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > From which we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-8 ALIGN=MIDDLE  ALT=\"y+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8 ALIGN=MIDDLE  ALT=\"y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-6 ALIGN=MIDDLE  ALT=\"y+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6 ALIGN=MIDDLE  ALT=\"y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Discard the negative solutions as the lengths of the rectangle sides can only be positive.<BR>\n" );
document.write( "So we have:<BR>\n" );
document.write( "y = 6 or 8 and x = 8 or 6<BR>\n" );
document.write( "The dimensions of the rectangle would be:<BR>\n" );
document.write( "Length = 8m and width = 6m<BR>\n" );
document.write( "Please note that while we solved only for y, the x-value is obtained by substituting y = 8 into eqation 1):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay+=+48 ALIGN=MIDDLE  ALT=\"x%2Ay+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8 ALIGN=MIDDLE  ALT=\"y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%288%29+=+48 ALIGN=MIDDLE  ALT=\"x%2A%288%29+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Dividing both sides by 8.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );