document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93150>Question 93150</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321186184/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Problem:\r<BR>\n" );
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document.write( "One leg of a right triangle has a length of 3m.  The other sides have lengths that are consecutive integers.  Find these lenths.\r<BR>\n" );
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document.write( "The other leg is ____ m<BR>\n" );
document.write( "The length of the hypotenuses is ____m\r<BR>\n" );
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document.write( "I get the consecutive inegers n, n+1<BR>\n" );
document.write( "and if I use the formula a^2 + b^2 = c^2 - I don't know what<BR>\n" );
document.write( "to plug in for c.  I've been shown several ways, and now<BR>\n" );
document.write( "I'm just confused.<BR>\n" );
document.write( "Thanks!!!\r<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 #67784 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=67784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, on this problem you do have to make at least one assumption:<BR>\n" );
document.write( "The given side of 3 meters is (or is not) the hypotenuse.<BR>\n" );
document.write( "If you assume that it is the hypotenuse, it is therefore the longest of the three sides of the right triangle.<BR>\n" );
document.write( "Since the other two sides are consective integers and each is less then 3, they can only be 1 and 2 mters in length.<BR>\n" );
document.write( "Well, as soon as you apply the Pythagorean theorem, you soon see that this cannot be so, because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2 ALIGN=MIDDLE  ALT=\"3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2+%2B+2%5E2 ALIGN=MIDDLE  ALT=\"1%5E2+%2B+2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So the 3-meter side is one of the legs, right?<BR>\n" );
document.write( "Now you have a choice: Is it the shorter leg or the longer leg (not the hypotenuse)?<BR>\n" );
document.write( "Let's try the shorter leg.<BR>\n" );
document.write( "So the hypotenuse, being the longest side must be n+1 and the other leg must be n. Applying the Pythagorean theorem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%5E2+=+n%5E2+%2B+3%5E2 ALIGN=MIDDLE  ALT=\"%28n%2B1%29%5E2+=+n%5E2+%2B+3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n%2B1+=+n%5E2+%2B+9 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n%2B1+=+n%5E2+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%2B1+=+9 ALIGN=MIDDLE  ALT=\"2n%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=2n+=+8 ALIGN=MIDDLE  ALT=\"2n+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+4 ALIGN=MIDDLE  ALT=\"n+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1+=+5 ALIGN=MIDDLE  ALT=\"n%2B1+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the hypotenuse is 5 meters,and the other leg is 4 meters.\r<BR>\n" );
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document.write( "If you were familiar with Pythagorean triplets, you could easily have guessed this result.\r<BR>\n" );
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