document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078089>Question 1078089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the hypotenuse of a right triangle is 1 inch longer than the longer of the two legs. The shorter leg is 7 inches. Find the length of the hypotenuse </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692554 by </B><A HREF=/tutors/aboutme.mpl?userid=themasterofcircuits><B>themasterofcircuits(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=themasterofcircuits><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=themasterofcircuits><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=692554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let b denote the longer leg, a denote the shorter leg, and c denote the hypotenuse<BR>\n" );
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document.write( "c=b+1 (1)<BR>\n" );
document.write( "a=7 (2)<BR>\n" );
document.write( "Pythagorean theorem:a^2+b^2=c^2 (3)\r<BR>\n" );
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document.write( "We have 3 equations and only 2 unknowns, so let's solve them:\r<BR>\n" );
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document.write( "First, let's solve for b by substituting (1) and (2) into (3):\r<BR>\n" );
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document.write( "(7)^2+b^2=(b+1)^2<BR>\n" );
document.write( "49+b^2=b^2+2b+1<BR>\n" );
document.write( "49=2b+1<BR>\n" );
document.write( "2b=48<BR>\n" );
document.write( "b=24\r<BR>\n" );
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document.write( "Now we can plug a=7 and b=24 into (3):\r<BR>\n" );
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document.write( "c^2=7^2+24^2<BR>\n" );
document.write( "c^2=625<BR>\n" );
document.write( "[c=25]\r<BR>\n" );
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document.write( "Hence, the hypotenuse is 25 inches. </SPAN>\n" );
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