document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697336>Question 697336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the area of a right isosceles triangle is 4, how long are its sides? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429902 by </B><A HREF=/tutors/aboutme.mpl?userid=Positive_EV><B>Positive_EV(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Positive_EV><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=Positive_EV><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=429902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of a triangle is equal to (1/2)*base*height. For a right triangle, the base and the height are the legs.\r<BR>\n" );
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document.write( "Since this is an isosceles triangle, both legs are the same length. Let L = the length of a leg:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2AL%2AL+=+4 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2AL%2AL+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > - divide both sides by 1/2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2+=+8 ALIGN=MIDDLE  ALT=\"L%5E2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > - take the square root of both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+sqrt%288%29+=+2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"L+=+sqrt%288%29+=+2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The legs are both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. For the hypotenuse, you can use the Pythagorean theorem:\r<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+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b+=+2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"a+=+b+=+2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%282%29%29%5E2%2B%282%2Asqrt%282%29%29%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%282%29%29%5E2%2B%282%2Asqrt%282%29%29%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+%2B+8+=+c%5E2 ALIGN=MIDDLE  ALT=\"8+%2B+8+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+c%5E2 ALIGN=MIDDLE  ALT=\"16+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, take the square root of both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+c ALIGN=MIDDLE  ALT=\"4+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The legs of the right triangle are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the hypotenuse is 4.\r<BR>\n" );
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document.write( "Follow-up edit: In this particular case, there are other ways to find the third side given the legs. Since this is a right isosceles (45-45-90) triangle, the ratios of the sides are going to be 1:1:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, another way to find the hypotenuse is to multiply the length of a leg by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which will also give 4 for the hypotenuse.\r<BR>\n" );
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document.write( "This specific method only works for right isosceles triangles, though. There's one other special case like this -- if you know the angles are 30, 60, and 90 degrees, the ratios of the sides are 1:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:2. The Pythagorean theorem works on any right triangle -- if you know any two sides you can always find the third side of a right triangle with it. </SPAN>\n" );
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