document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255278>Question 255278</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is x + 4<BR>\n" );
document.write( "The width of a rectangle is x - 1<BR>\n" );
document.write( "The perimeter is 46 cm\r<BR>\n" );
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document.write( "Calculate the length of the diagonal of the rectangle\r<BR>\n" );
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document.write( "Please help?! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187547 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=187547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we know the length and width of a rectangle we can use the Pythagorean Theorem to find the diagonal. So we will start by finding the length and width.<br><BR>\n" );
document.write( "We should know that the perimeter of a rectangle is the sum of the two lengths and the two widths. We are told that the perimeter is 46 and that the length is x+4 and the width is x-1. So:<BR>\n" );
document.write( "46 = x+4 + x+4 + x-1 + x-1<BR>\n" );
document.write( "We can solve this for x. Simplifying the right side we get:<BR>\n" );
document.write( "46 = 4x + 6<BR>\n" );
document.write( "Subtracting 6 from each side we get:<BR>\n" );
document.write( "40 = 4x<BR>\n" );
document.write( "Dividing both sides by 4 we get:<BR>\n" );
document.write( "10 = x<br><BR>\n" );
document.write( "So the length, x+4, is 14 and the width, x-1, is 9. The length and width of a rectangle and the diagonal of a rectangle form a right triangle with the diagonal as the hypotenuse. So we can use the Pythagorean Theorem to find the length of the diagonal. If d is the length of the diagonal then:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2+=+14%5E2+%2B+9%5E2 ALIGN=MIDDLE  ALT=\"d%5E2+=+14%5E2+%2B+9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying the right side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2+=+196+%2B+81 ALIGN=MIDDLE  ALT=\"d%5E2+=+196+%2B+81\"   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+=+277 ALIGN=MIDDLE  ALT=\"d%5E2+=+277\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving for d we get:<BR>\n" );
document.write( "d = +-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28277%29 ALIGN=MIDDLE  ALT=\"sqrt%28277%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since d is the length of the diagonal, we will discard the negative value. So the length of the diagonal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28277%29 ALIGN=MIDDLE  ALT=\"sqrt%28277%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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