document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=597607>Question 597607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 2 cm less than twice the shorter side. The longer side is 2 cm longer than the shorter side. How long is the hypotenuse? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378286 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "Since this is a right triangle, we will use the Pythagorean Equation to find the lengths of the hypotenuse.<BR>\n" );
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document.write( "[I] Define the variables<BR>\n" );
document.write( "Call a the length of the short leg.<BR>\n" );
document.write( "Call b the length of the long leg.<BR>\n" );
document.write( "Call c the hypotenuse.<BR>\n" );
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document.write( "[II] Create equation based on the given relationships<BR>\n" );
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document.write( "By the Pythagorean Theorem, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In algebra, \"the hypotenuse is 2 cm less than twice the shorter side\" can be written as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=2%2Aa-2 ALIGN=MIDDLE  ALT=\"c=2%2Aa-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Likewise, we can write \"the longer side is 2 cm longer that the shorter side\" as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=a%2B2 ALIGN=MIDDLE  ALT=\"b=a%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "[III] Solve the system of equations<BR>\n" );
document.write( "Substitute a+2 for b and 2*a-2 for c in the Pythagorean Equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B%28a%2B2%29%5E2=%282%2Aa-2%29%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2B%28a%2B2%29%5E2=%282%2Aa-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use the distributive property to clear the parentheses.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B%28a%5E2%2B4a%2B4%29=4%2Aa%5E2-8a%2B4 ALIGN=MIDDLE  ALT=\"a%5E2%2B%28a%5E2%2B4a%2B4%29=4%2Aa%5E2-8a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify and solve for a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2%2B4a%2B4=4%2Aa%5E2-8a%2B4 ALIGN=MIDDLE  ALT=\"2a%5E2%2B4a%2B4=4%2Aa%5E2-8a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2a%5E2%2B12a=0 ALIGN=MIDDLE  ALT=\"-2a%5E2%2B12a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Factor the quadratic polynomial on the left side of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2A%28a-6%29=0 ALIGN=MIDDLE  ALT=\"-2%2A%28a-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By the Zero Product Property, is -2 times (a-6) equals zero, then (a-6) must equal zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-6=0 ALIGN=MIDDLE  ALT=\"a-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The equation a=6 means that the shorter leg of the triangle is 6 cm.<BR>\n" );
document.write( "The longer leg is a+2 = 6+2 = 8 cm.<BR>\n" );
document.write( "The hypotenuse is 2*a-2 = 2(6)-2 = 10 cm.<BR>\n" );
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document.write( "[IV] Check your work<BR>\n" );
document.write( "Do these values satisfy a right triangle?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%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=%286%29%5E2%2B%288%29%5E2=%2810%29%5E2 ALIGN=MIDDLE  ALT=\"%286%29%5E2%2B%288%29%5E2=%2810%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2B64=100 ALIGN=MIDDLE  ALT=\"36%2B64=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100=100 ALIGN=MIDDLE  ALT=\"100=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Correct!<BR>\n" );
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document.write( "THe hypotenuse is 10 cm.<BR>\n" );
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document.write( "I hope this helps!<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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