document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85290>Question 85290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the missing side in the triangle using pythagorean theorem, give answer as a simplified radical\r<BR>\n" );
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document.write( "x,2x,15\r<BR>\n" );
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document.write( "\"Find X\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61480 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=61480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given: A triangle having the sides x, 2x, and 15.  The problem says to use the Pythagorean<BR>\n" );
document.write( "theorem to find the value of x. (This means that the given triangle is a right triangle<BR>\n" );
document.write( "since the Pythagorean theorem only applies to right triangles.)<BR>\n" );
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document.write( "The way this problem is stated, there are two possible answers depending on which side you <BR>\n" );
document.write( "assume is the long side (hypotenuse). The side x cannot be the hypotenuse because it is shorter<BR>\n" );
document.write( "than the side 2x.  Therefore, there are two possibilities for the hypotenuse.  Either the<BR>\n" );
document.write( "hypotenuse is 2x or it is 15.<BR>\n" );
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document.write( "Let's first assume that the hypotenuse is 2x. That means that one leg is x and the other is<BR>\n" );
document.write( "15.<BR>\n" );
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document.write( "By the Pythagorean theorem, square each of the legs, add these two squares, and set that <BR>\n" );
document.write( "sum equal to the square of the hypotenuse. In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+15%5E2+=+%282x%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+15%5E2+=+%282x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The square of 15 is 225 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E2+=+4x%5E2 ALIGN=MIDDLE  ALT=\"%282x%29%5E2+=+4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute these into the equation and<BR>\n" );
document.write( "it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+225+=+4x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+225+=+4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225+=+3x%5E2 ALIGN=MIDDLE  ALT=\"225+=+3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 3 and it further reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75+=+x%5E2 ALIGN=MIDDLE  ALT=\"75+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next take the square root of both sides and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%2875%29+=+sqrt%2825%2A3%29+=+sqrt%2825%29%2Asqrt%283%29+=+5%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%2875%29+=+sqrt%2825%2A3%29+=+sqrt%2825%29%2Asqrt%283%29+=+5%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice the steps involved in simplifying the radical to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+5%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the<BR>\n" );
document.write( "first possible answer.<BR>\n" );
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document.write( "But we said that the possibility exists that the hypotenuse is 15. In this case the two<BR>\n" );
document.write( "legs are x and 2x. Applying the Pythagorean theorem to this problem results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%282x%29%5E2+=+15%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%282x%29%5E2+=+15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Again substituting for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E2 ALIGN=MIDDLE  ALT=\"%282x%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%5E2 ALIGN=MIDDLE  ALT=\"15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > changes the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x%5E2+=+225 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x%5E2+=+225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Adding the two term on the left side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+=+225 ALIGN=MIDDLE  ALT=\"5x%5E2+=+225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 5 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+45 ALIGN=MIDDLE  ALT=\"x%5E2+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then take the square root of both sides and you end up with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%2845%29+=+sqrt%289%2A5%29+=+sqrt%289%29%2Asqrt%285%29+=+3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%2845%29+=+sqrt%289%2A5%29+=+sqrt%289%29%2Asqrt%285%29+=+3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the second possible answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x+=+3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Which answer fits is dependent on which side is presumed to be the hypotenuse.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and why the possibility exists for two answers.<BR>\n" );
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