document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=852051>Question 852051</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 <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 #513106 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=513106\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I cannot decide if this is a trick geometry question, or an attempt at mixing algebra and geometry.<BR>\n" );
document.write( "With the length of the hypotenuse, the isosceles right triangle is uniquely determined, so we do not need any other length.<BR>\n" );
document.write( "The variable <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > shows up, unneeded, adding nothing but confusion.<BR>\n" );
document.write( "The problem says that the length of one side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > , but does not ask to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > . If we tried to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since the problem does not specify if the side measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one leg of the triangle or the hypotenuse, we would find two possible values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but it would still be the same triangle, with the same perimeter.<BR>\n" );
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document.write( "AS A TRICK PROBLEM TO BE SOLVED THE SMART WAY:<BR>\n" );
document.write( "An isosceles right angled triangle has two equally long sides, called legs, opposite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%5Eo ALIGN=MIDDLE  ALT=\"45%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angles.<BR>\n" );
document.write( "If we call the length of the hypotenuse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the Pythagorean theorem tells has that the length of each leg will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Lsqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"Lsqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=leg%5E2%2Bleg%5E2=L%5E2 ALIGN=MIDDLE  ALT=\"leg%5E2%2Bleg%5E2=L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2leg%5E2=L%5E2 ALIGN=MIDDLE  ALT=\"2leg%5E2=L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=leg%5E2=L%5E2%2F2 ALIGN=MIDDLE  ALT=\"leg%5E2=L%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=leg=L%2Fsqrt%282%29=Lsqrt%282%29%2F2 ALIGN=MIDDLE  ALT=\"leg=L%2Fsqrt%282%29=Lsqrt%282%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, the perimeter is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2BLsqrt%282%29%2F2%2BLsqrt%282%29%2F2=L%2BLsqrt%282%29 ALIGN=MIDDLE  ALT=\"L%2BLsqrt%282%29%2F2%2BLsqrt%282%29%2F2=L%2BLsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So if the hypotenuse measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12cm ALIGN=MIDDLE  ALT=\"12cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the perimeter is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2B12sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"%2812%2B12sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "PRETENDING THAT THIS IS AN ALGEBRA PROBLEM,<BR>\n" );
document.write( "and that they meant that the side with a length of (x+2) cm is not the hypotenuse.<BR>\n" );
document.write( "If the length of one of the legs of the right isosceles triangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm,<BR>\n" );
document.write( "the length of the other leg of the right isosceles triangle is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm.<BR>\n" );
document.write( "Then, the Pythagorean theorem says that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%2B%28x%2B2%29%5E2=12%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2B%28x%2B2%29%5E2=12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B2%29%5E2=12%5E2 ALIGN=MIDDLE  ALT=\"2%28x%2B2%29%5E2=12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2=12%5E2%2F2 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2=12%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2=2%2A6%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2=2%2A6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=6sqrt%282%29 ALIGN=MIDDLE  ALT=\"x%2B2=6sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is the length (in cm) of each leg of the isosceles right triangle, and that is all we need, because we have not been asked to find the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then, the perimeter (in cm) would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2B6sqrt%282%29%2B6sqrt%282%29=12%2B12sqrt%282%29 ALIGN=MIDDLE  ALT=\"12%2B6sqrt%282%29%2B6sqrt%282%29=12%2B12sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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