document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=387378>Question 387378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the perimiter of a right triangle is 12. the lengths of the legs of the triangle are 3 and x. the length of the hypotenuse is y.<BR>\n" );
document.write( "how can i set up a system of equation that could be used to find the hypotenuse and the other of the right triangle?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #273816 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=273816\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  the perimeter of a right triangle is 12. <BR>\n" );
document.write( "the lengths of the legs of the triangle are 3 and x. <BR>\n" );
document.write( "the length of the hypotenuse is y.<BR>\n" );
document.write( "how can i set up a system of equation that could be used to find the hypotenuse and the other of the right triangle?<BR>\n" );
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document.write( "Express the hypotenuse in terms of \"x\" using Pythagoras.<BR>\n" );
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document.write( "y^2 = 3^2 + x^2<BR>\n" );
document.write( "y = sqrt(9+x^2)<BR>\n" );
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document.write( "Then the perimeter is 3 + x + sqrt(9+x^2) = 12<BR>\n" );
document.write( "Solve for \"x\":<BR>\n" );
document.write( "x + sqrt(9+x^2) = 9<BR>\n" );
document.write( "sqrt(9+x^2) = 9-x<BR>\n" );
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document.write( "Square both sides to get:<BR>\n" );
document.write( "9+x^2 = 81-18x+x^2<BR>\n" );
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document.write( "9 = 81-18x<BR>\n" );
document.write( "18x = 72<BR>\n" );
document.write( "x = 4<BR>\n" );
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document.write( "The sides are 3,4,y<BR>\n" );
document.write( "y = sqrt(9+x^2) = sqrt(9+16) = 5<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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