document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119104>Question 119104</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of one leg of a right triangle is 1 in. more than the other. If the length of the hypotenuse is 3 in., what are the lengths of the legs? round to the nearest thousandth of an inch. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87212 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=87212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the shorter leg of the triangle be x, then the longer leg is x + 1.\r<BR>\n" );
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document.write( "Using Pythagoras' formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2B%28x%2B1%29%5E2%29=3 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2B%28x%2B1%29%5E2%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Square both sides:\r<BR>\n" );
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document.write( "Expand the binomial and simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2%2B2x%2B1=9 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B2x%2B1=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B2x=8 ALIGN=MIDDLE  ALT=\"2x%5E2%2B2x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx=4 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx-4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the quadratic with the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B-+sqrt%28+1%2B16+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%2B16+%29%29%2F%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=x+=+%28-1+%2B-+sqrt%28+17+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+17+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+-+sqrt%28+17+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+-+sqrt%28+17+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is clearly < 0, and a negative number representing the length of the side of a triangle is nonsense, so we can exclude this root of the equation as an answer to our problem.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-1+%2B+sqrt%28+17+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B+sqrt%28+17+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is then the exact representation of the length of the short side of the triangle, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%28-1+%2B-+sqrt%28+17+%29%29%2F%282%29%29%2B1=%281+%2B-+sqrt%28+17+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28%28-1+%2B-+sqrt%28+17+%29%29%2F%282%29%29%2B1=%281+%2B-+sqrt%28+17+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the exact representation of the length of the longer side.\r<BR>\n" );
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document.write( "However, you were asked to express your answer as a decimal to the nearest thousanth of an inch.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2817%29 ALIGN=MIDDLE  ALT=\"sqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is approximately 4.1231.  Subtracting 1 and dividing by 2 yields 1.5615 which rounds to 1.562, for the short side, and then adding 1 would give 2.562 for the long side.\r<BR>\n" );
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document.write( "Note:  It is completely inappropriate to express the answer to this problem with the precision (nearest 1000th) asked.  The results of calculations involving measurements should never be expressed with any greater precision than the LEAST precise measurement in the given values.  Had the problem been worded thus:  <i>\"The length of one leg of a right triangle is 1.000 in. more than the other. If the length of the hypotenuse is 3.000 in., what are the lengths of the legs? round to the nearest thousandth of an inch.\"</i>  Then the requested precision would have been both appropriate and unnecessary to request.\r<BR>\n" );
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document.write( "The difference between saying that the side of the triangle measures 1 inch and saying that it measures 1.000 inch is vast.  Saying that the measure is 1 inch only guarantees that the measurement is somewhere on the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%3C=x%3C1.5 ALIGN=MIDDLE  ALT=\"0.5%3C=x%3C1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, whereas saying that the measure is 1.000 inch restricts the interval to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9995%3C=x%3C1.0005 ALIGN=MIDDLE  ALT=\"0.9995%3C=x%3C1.0005\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, although 1.562 inches and 2.562 inches are the values the question required, the correct values, given the precision of the given measurements, are 2 inches and 3 inches. </SPAN>\n" );
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