document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109800>Question 109800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the diagonal of a rectangle with 5 in. width and 7 in. length </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80005 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=80005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you sketch a rectangle that has a length of 7 inches and a width of 5 inches, and you then<BR>\n" );
document.write( "draw in a diagonal, you will see that the diagonal splits the rectangle into two right triangles.<BR>\n" );
document.write( "In both these triangles the diagonal is the long side, so it is the hypotenuse of each triangle,<BR>\n" );
document.write( "and the two legs of each triangle are 5 inches and 7 inches.<BR>\n" );
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document.write( "Because the two triangles are right triangles, the Pythagorean theorem applies. This theorem<BR>\n" );
document.write( "says that the sum of the squares of the two legs of a right triangle are equal to the square of<BR>\n" );
document.write( "the hypotenuse of the triangle. In equation form this can be written as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2+%2B+B%5E2+=+H%5E2 ALIGN=MIDDLE  ALT=\"A%5E2+%2B+B%5E2+=+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where A and B are the two legs of the right triangle and H is the hypotenuse. We can then <BR>\n" );
document.write( "substitute 5 for one of the legs and 7 for the other to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2+%2B+7%5E2+=+H%5E2 ALIGN=MIDDLE  ALT=\"5%5E2+%2B+7%5E2+=+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Squaring out the two terms on the left side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+%2B+49+=+H%5E2 ALIGN=MIDDLE  ALT=\"25+%2B+49+=+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Adding the two terms on the left results in reducing the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=74+=+H%5E2 ALIGN=MIDDLE  ALT=\"74+=+H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can then solve for the length of the hypotenuse (H) by taking the square root of both<BR>\n" );
document.write( "sides to get that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+sqrt%2874%29 ALIGN=MIDDLE  ALT=\"H+=+sqrt%2874%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Calculator time ... the square root of 74 is 8.602325267. So the length of the hypotenuse is<BR>\n" );
document.write( "8.602325267 inches, and this is the answer to your problem.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better and to see a way that you can<BR>\n" );
document.write( "solve it.<BR>\n" );
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