document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=837682>Question 837682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an isosceles right-angled triangle has one side length of (x+2) cm and the length of the hypotenuse is 12 cm. find the perimeter of the triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #504709 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=504709\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is an isosceles right triangle.<BR>\n" );
document.write( "the legs are of equal length.<BR>\n" );
document.write( "the length of 1 leg is equal to x + 2.<BR>\n" );
document.write( "in a right triangle, a^2 + b^2 = c^2<BR>\n" );
document.write( "let a = x + 2<BR>\n" );
document.write( "let b = x + 2<BR>\n" );
document.write( "let c = 12<BR>\n" );
document.write( "the formula becomes:<BR>\n" );
document.write( "(x+2)^2 + (x+2)^2 = 12^2<BR>\n" );
document.write( "this can be simplified to:<BR>\n" );
document.write( "2 * (x+2)^2 = 144 which can be further simplified to:<BR>\n" );
document.write( "(x+2)^2 = 72<BR>\n" );
document.write( "take the square root of both sides of this equation to get:<BR>\n" );
document.write( "sqrt((x+2)^2) = sqrt(72)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "x+2 = +/- sqrt(72)<BR>\n" );
document.write( "subtract 2 from both sides of this equation to get:<BR>\n" );
document.write( "x = -2 +/- sqrt(72)<BR>\n" );
document.write( "you get 2 possible values of x.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "x = -10.48528137 or:<BR>\n" );
document.write( "x = 6.485281374\r<BR>\n" );
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document.write( "since x can't be negative, the only possible solution is x = 6.485281374.<BR>\n" );
document.write( "this means that (x+2) is equal to 8.485281374<BR>\n" );
document.write( "to confirm this solution is good, 2 * (8.485281374)^2 to see what it gets you.<BR>\n" );
document.write( "it gets you 144 which is the hypotenuse squared, as it should, so the solution is good.<BR>\n" );
document.write( "each leg of the triangle is equal to 8.485281374 and the hypotenuse is equal to 12.<BR>\n" );
document.write( "the perimeters is equal to 2 * the legs plus the hypotenuse which makes the perimeter of the triangle equal to 28.97056275 cm  which you can round as much as you like.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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