document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144667>Question 144667</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132319284/algebrahomeworkh>Prealgebra & Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the legs of a right triangle is 17 in. The longer leg is 2 more than twice the shorter. Th hypotenuse is 13 in. Find the length of each leg. Isn't the formula for a right triangle a^2 +b^2=c^2? From what I understand this is the way I would write to solve, but it doesn't make sense to me.\r<BR>\n" );
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document.write( "17=a^2+b^2+2<BR>\n" );
document.write( "a^2+b^2= 13^2\r<BR>\n" );
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document.write( "Thanks for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105427 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=105427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Length of one leg: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Length of the other leg: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Assume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the long leg, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+2a+%2B+2 ALIGN=MIDDLE  ALT=\"b+=+2a+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (2 more than twice the shorter)\r<BR>\n" );
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document.write( "Sum of the lengths of the legs: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+=+17 ALIGN=MIDDLE  ALT=\"a+%2B+b+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2a%2B2 ALIGN=MIDDLE  ALT=\"b=2a%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B2a%2B2=17 ALIGN=MIDDLE  ALT=\"a%2B2a%2B2=17\"   DISABLED_style= \"max-width:90%; height:auto;\" > by substitution.\r<BR>\n" );
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document.write( "Collect like terms and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2B2=17 ALIGN=MIDDLE  ALT=\"3a%2B2=17\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a=15 ALIGN=MIDDLE  ALT=\"3a=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+b+=+17 ALIGN=MIDDLE  ALT=\"5+%2B+b+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=12 ALIGN=MIDDLE  ALT=\"b=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2%2B12%5E2=25%2B144=169=13%5E2 ALIGN=MIDDLE  ALT=\"5%5E2%2B12%5E2=25%2B144=169=13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Checks.\r<BR>\n" );
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document.write( "Note that if we had assumed in the beginning that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > was the longer leg, the result would have been that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=12 ALIGN=MIDDLE  ALT=\"a=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5 ALIGN=MIDDLE  ALT=\"b=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > -- same answer for all practical purposes. </SPAN>\n" );
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